A015843 -id:A015843

A015858

Numbers k such that phi(k) | sigma(k + 11).

+10
6

1, 2, 3, 4, 6, 8, 9, 10, 12, 13, 16, 18, 19, 20, 24, 35, 36, 45, 49, 51, 74, 77, 79, 84, 91, 104, 108, 113, 124, 129, 130, 144, 148, 180, 198, 219, 224, 279, 286, 308, 380, 407, 434, 435, 459, 490, 584, 609, 610, 616, 624, 627, 628, 640, 644, 679, 779

(list; graph; refs; listen; history; text; internal format)

OFFSET

1,2

LINKS

Harvey P. Dale, Table of n, a(n) for n = 1..1000

MATHEMATICA

Select[Range[800], Divisible[DivisorSigma[1, #+11], EulerPhi[#]]&] (* Harvey P. Dale, Aug 01 2016 *)

PROG

(PARI) is(n)=!(sigma(n+11)%eulerphi(n)) \\ Charles R Greathouse IV, Sep 25 2012

(Magma) [n: n in [1..900] | DivisorSigma(1, n+11) mod EulerPhi(n) eq 0]; // G. C. Greubel, Dec 13 2018

CROSSREFS

Cf. A015834 (m=1), A015837 (m=2), A015840 (m=3), A015841 (m=4), A015843 (m=5), A015844 (m=6), A015845 (m=7), A015851 (m=8), A015853 (m=9), A015856 (m=10), this sequence (m=11), A015859 (m=12), A015860 (m=13).

KEYWORD

nonn

AUTHOR

Robert G. Wilson v

EXTENSIONS

Missing a(1)=1 inserted by Sean A. Irvine, Dec 13 2018

STATUS

approved

A015859

Numbers k such that phi(k) | sigma(k + 12).

+10
6

1, 2, 3, 10, 12, 14, 15, 16, 18, 21, 26, 30, 35, 39, 42, 44, 54, 65, 75, 76, 90, 108, 123, 126, 153, 156, 165, 218, 234, 252, 270, 364, 366, 370, 396, 462, 474, 494, 508, 525, 540, 558, 615, 620, 630, 646, 702, 732, 814, 852, 858, 918, 980, 1022, 1044

(list; graph; refs; listen; history; text; internal format)

OFFSET

1,2

LINKS

G. C. Greubel, Table of n, a(n) for n = 1..500

MATHEMATICA

Select[Range[1100], Divisible[DivisorSigma[1, #+12], EulerPhi[#]]&] (* Harvey P. Dale, Jun 01 2018 *)

PROG

(PARI) is(n)=!(sigma(n+12)%eulerphi(n)) \\ Charles R Greathouse IV, Sep 25 2012

(Magma) [n: n in [1..900] | DivisorSigma(1, n+12) mod EulerPhi(n) eq 0]; // G. C. Greubel, Dec 13 2018

CROSSREFS

Cf. A015834 (m=1), A015837 (m=2), A015840 (m=3), A015841 (m=4), A015843 (m=5), A015844 (m=6), A015845 (m=7), A015851 (m=8), A015853 (m=9), A015856 (m=10), A015858 (m=11), this sequence (m=12), A015860 (m=13).

KEYWORD

nonn

AUTHOR

Robert G. Wilson v

EXTENSIONS

Missing a(1)=1 inserted by Sean A. Irvine, Dec 13 2018

STATUS

approved

A015860

Numbers k such that phi(k) | sigma(k + 13).

+10
6

1, 2, 4, 6, 7, 8, 9, 10, 11, 15, 20, 25, 27, 34, 38, 41, 42, 44, 56, 57, 64, 66, 80, 82, 120, 122, 128, 146, 152, 155, 164, 176, 204, 222, 237, 310, 330, 331, 342, 377, 378, 400, 427, 460, 465, 490, 500, 504, 560, 602, 610, 626, 704, 722, 770, 817, 861

(list; graph; refs; listen; history; text; internal format)

OFFSET

1,2

LINKS

G. C. Greubel, Table of n, a(n) for n = 1..500

MATHEMATICA

Select[Range[900], Mod[DivisorSigma[1, #+13], EulerPhi[#]]==0 &] (* G. C. Greubel, Dec 13 2018 *)

PROG

(PARI) is(n)=!(sigma(n+13)%eulerphi(n)) \\ Charles R Greathouse IV, Sep 25 2012

(Magma) [n: n in [1..900] | DivisorSigma(1, n+13) mod EulerPhi(n) eq 0]; // G. C. Greubel, Dec 13 2018

CROSSREFS

Cf. A015834 (m=1), A015837 (m=2), A015840 (m=3), A015841 (m=4), A015843 (m=5), A015844 (m=6), A015845 (m=7), A015851 (m=8), A015853 (m=9), A015856 (m=10), A015858 (m=11), A015859 (m=12), this sequence (m=13).

KEYWORD

nonn

AUTHOR

Robert G. Wilson v

EXTENSIONS

Missing a(1)=1 inserted by Sean A. Irvine, Dec 13 2018

STATUS

approved

A015853

Numbers k such that phi(k) | sigma(k + 9).

+10
5

1, 2, 3, 4, 5, 6, 10, 12, 13, 14, 21, 24, 26, 30, 31, 37, 42, 45, 48, 50, 57, 60, 68, 76, 78, 96, 105, 111, 133, 156, 168, 175, 181, 196, 200, 215, 273, 286, 288, 290, 310, 320, 336, 350, 361, 369, 381, 399, 406, 420, 450, 465, 543, 585, 600, 612, 656, 740

(list; graph; refs; listen; history; text; internal format)

OFFSET

1,2

LINKS

G. C. Greubel, Table of n, a(n) for n = 1..1000

MATHEMATICA

Select[Range[1000], Divisible[DivisorSigma[1, #+9], EulerPhi[#]] &] (* Amiram Eldar, Dec 13 2018 *)

PROG

(PARI) is(n)=!(sigma(n+9)%eulerphi(n)) \\ Charles R Greathouse IV, Sep 25 2012

(Magma) [n: n in [1..900] | DivisorSigma(1, n+9) mod EulerPhi(n) eq 0]; // G. C. Greubel, Dec 13 2018

CROSSREFS

Cf. A015834 (m=1), A015837 (m=2), A015840 (m=3), A015841 (m=4), A015843 (m=5), A015844 (m=6), A015845 (m=7), A015851 (m=8), this sequence (m=9), A015856 (m=10), A015858 (m=11), A015859 (m=12), A015860 (m=13).

KEYWORD

nonn

AUTHOR

Robert G. Wilson v

EXTENSIONS

Missing a(1)=1 inserted by Sean A. Irvine, Dec 13 2018

STATUS

approved

A015856

Numbers k such that phi(k) | sigma(k + 10).

+10
5

1, 2, 3, 4, 5, 7, 12, 13, 14, 20, 28, 29, 32, 36, 44, 45, 52, 53, 56, 60, 66, 77, 84, 86, 104, 105, 108, 110, 123, 130, 144, 172, 221, 228, 238, 270, 287, 312, 342, 366, 380, 385, 396, 441, 468, 558, 584, 585, 588, 644, 672, 750, 754, 760, 854, 864

(list; graph; refs; listen; history; text; internal format)

OFFSET

1,2

LINKS

G. C. Greubel, Table of n, a(n) for n = 1..1000

MATHEMATICA

Select[Range[1000], Divisible[DivisorSigma[1, #+10], EulerPhi[#]] &] (* Amiram Eldar, Dec 13 2018 *)

PROG

(PARI) is(n)=!(sigma(n+10)%eulerphi(n)) \\ Charles R Greathouse IV, Sep 25 2012

(Magma) [n: n in [1..900] | DivisorSigma(1, n+10) mod EulerPhi(n) eq 0]; // G. C. Greubel, Dec 13 2018

CROSSREFS

Cf. A015834 (m=1), A015837 (m=2), A015840 (m=3), A015841 (m=4), A015843 (m=5), A015844 (m=6), A015845 (m=7), A015851 (m=8), A015853 (m=9), this sequence (m=10), A015858 (m=11), A015859 (m=12), A015860 (m=13).

KEYWORD

nonn

AUTHOR

Robert G. Wilson v

EXTENSIONS

Missing a(1)=1 inserted by Sean A. Irvine, Dec 13 2018

STATUS

approved