A320113 -id:A320113

The OEIS is supported by the many generous donors to the OEIS Foundation.

Search: a320113 -id:a320113

Displaying 1-4 of 4 results found.

page 1

A320115

Filter sequence for counting the residue classes mod 4 of divisors of n.

+10
6

1, 2, 3, 4, 5, 6, 3, 7, 8, 9, 3, 10, 5, 6, 11, 12, 5, 13, 3, 14, 11, 6, 3, 15, 16, 9, 11, 10, 5, 17, 3, 18, 11, 9, 11, 19, 5, 6, 11, 20, 5, 17, 3, 10, 21, 6, 3, 22, 8, 23, 11, 14, 5, 17, 11, 15, 11, 9, 3, 24, 5, 6, 25, 26, 27, 17, 3, 14, 11, 17, 3, 28, 5, 9, 25, 10, 11, 17, 3, 29, 30, 9, 3, 24, 27, 6, 11, 15, 5, 31, 11, 10, 11, 6, 11, 32, 5, 13, 25, 33, 5, 17, 3, 20

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

OFFSET

1,2

COMMENTS

Restricted growth sequence transform of A320114.

For all i, j:

A319994(i) = A319994(j) => a(i) = a(j),

A320004(i) = A320004(j) => a(i) = a(j),

a(i) = a(j) => A002654(i) = A002654(j).

LINKS

Antti Karttunen, Table of n, a(n) for n = 1..100000

PROG

(PARI)

up_to = 100000;

A320114(n) = { my(m=1); fordiv(n, d, if(d>1, m *= prime(1+(d%4)))); (m); };

rgs_transform(invec) = { my(om = Map(), outvec = vector(length(invec)), u=1); for(i=1, length(invec), if(mapisdefined(om, invec[i]), my(pp = mapget(om, invec[i])); outvec[i] = outvec[pp] , mapput(om, invec[i], i); outvec[i] = u; u++ )); outvec; };

v320115 = rgs_transform(vector(up_to, n, A320114(n)));

A320115(n) = v320115[n];

CROSSREFS

Cf. A319994, A320004, A320109, A320113, A320114, A320117.

KEYWORD

nonn

AUTHOR

Antti Karttunen, Oct 06 2018

STATUS

approved

A320117

Filter sequence for counting the residue classes mod 6 of divisors of n.

+10
6

1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 5, 11, 7, 12, 13, 14, 5, 15, 7, 16, 17, 10, 5, 18, 19, 12, 20, 21, 5, 22, 7, 23, 13, 10, 24, 25, 7, 12, 17, 26, 5, 27, 7, 16, 28, 10, 5, 29, 30, 31, 13, 21, 5, 32, 24, 33, 17, 10, 5, 34, 7, 12, 35, 36, 24, 22, 7, 16, 13, 37, 5, 38, 7, 12, 39, 21, 24, 27, 7, 40, 41, 10, 5, 42, 24, 12, 13, 26, 5, 43, 44, 16, 17, 10, 24, 45, 7, 46, 28, 47, 5, 22, 7, 33

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

OFFSET

1,2

COMMENTS

Restricted growth sequence transform of A320116.

For all i, j:

A319717(i) = A319717(j) => a(i) = a(j),

A319996(i) = A319996(j) => a(i) = a(j),

A320113(i) = A320113(j) => a(i) = a(j),

a(i) = a(j) => A002324(i) = A002324(j).

LINKS

Antti Karttunen, Table of n, a(n) for n = 1..100000

PROG

(PARI)

up_to = 100000;

A320116(n) = { my(m=1); fordiv(n, d, if(d>1, m *= prime(1+(d%6)))); (m); };

v320117 = rgs_transform(vector(up_to, n, A320116(n)));

A320117(n) = v320117[n];

CROSSREFS

Cf. A319717, A319996, A320109, A320113, A320115, A320116.

KEYWORD

nonn

AUTHOR

Antti Karttunen, Oct 06 2018

STATUS

approved

A320109

Filter sequence for counting the residue classes mod 8 of divisors of n.

+10
5

1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 3, 11, 5, 12, 13, 14, 15, 16, 3, 17, 13, 6, 7, 18, 19, 10, 20, 21, 5, 22, 7, 23, 20, 24, 13, 25, 5, 6, 13, 26, 15, 22, 3, 11, 27, 12, 7, 28, 29, 30, 20, 17, 5, 31, 13, 32, 20, 10, 3, 33, 5, 12, 34, 35, 36, 31, 3, 37, 13, 22, 7, 38, 15, 10, 39, 11, 13, 22, 7, 40, 41, 24, 3, 33, 36, 6, 13, 18, 15, 42, 13, 21, 13, 12, 13, 43, 15, 44, 45, 46, 5, 31, 7, 26

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

OFFSET

1,2

COMMENTS

Restricted growth sequence transform of A320108.

For all i, j: a(i) = a(j) => A320115(i) = A320115(j).

LINKS

Antti Karttunen, Table of n, a(n) for n = 1..100000

PROG

(PARI)

up_to = 100000;

A320108(n) = { my(m=1); fordiv(n, d, if(d>1, m *= prime(1+(d%8)))); (m); };

v320109 = rgs_transform(vector(up_to, n, A320108(n)));

A320109(n) = v320109[n];

CROSSREFS

Cf. A320108, A320113, A320115, A320117.

KEYWORD

nonn

AUTHOR

Antti Karttunen, Oct 06 2018

STATUS

approved

A320112

a(n) = Product_{d|n, d>1} prime(1+(d mod 12)).

+10
3

1, 5, 7, 55, 13, 595, 19, 1265, 203, 2015, 37, 13090, 3, 475, 637, 13915, 13, 293335, 19, 509795, 3857, 5735, 37, 602140, 39, 75, 1421, 57475, 13, 28534415, 19, 320045, 7511, 2015, 9139, 12906740, 3, 475, 147, 128978135, 13, 27866825, 19, 1450955, 535717, 5735, 37, 13247080, 57, 30225, 637, 9075, 13, 34906865, 9139, 30404275, 3857, 2015, 37

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

OFFSET

1,2

LINKS

Antti Karttunen, Table of n, a(n) for n = 1..8192

FORMULA

a(n) = Product_{d|n, d>1} prime(1+(d mod 12)).

PROG

(PARI) A320112(n) = { my(m=1); fordiv(n, d, if(d>1, m *= prime(1+(d%12)))); (m); };

CROSSREFS

Cf. A319985, A320108, A320114, A320116.

Cf. A320113 (rgs-transform).