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Revision History for A354603

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Numbers k such that sum of distinct primes dividing k is equal to the sum of proper divisors of k+1.
(history; published version)

#10 by N. J. A. Sloane at Wed Sep 07 11:10:45 EDT 2022

STATUS

editing

approved

#9 by N. J. A. Sloane at Wed Sep 07 11:10:38 EDT 2022

NAME

Numbers k such that sum of distinct primes dividing k equals is equal to the sum of proper divisors of k+1.

STATUS

proposed

editing

Discussion

Wed Sep 07

11:10

N. J. A. Sloane: edited

#8 by Amiram Eldar at Fri Jul 08 07:49:07 EDT 2022

STATUS

editing

proposed

#7 by Amiram Eldar at Fri Jul 08 07:49:04 EDT 2022

DATA

3, 7, 14, 31, 127, 206, 2974, 8191, 19358, 20490, 131071, 147454, 286122, 289650, 292332, 441276, 524287, 909498, 1207358, 1657968, 1782540, 2490042, 3368860, 9274806, 11367402, 14107852, 16776156, 18589386, 22910988, 24450316, 26867718, 28959606, 32674506, 33163372

KEYWORD

nonn,more,changed

EXTENSIONS

More terms from Amiram Eldar, Jul 08 2022

STATUS

proposed

editing

#6 by Metin Sariyar at Fri Jul 08 07:18:16 EDT 2022

STATUS

editing

proposed

#5 by Metin Sariyar at Fri Jul 08 07:13:58 EDT 2022

MATHEMATICA

Select[Range[19358], Sum[f, {f, Select[Divisors[#], PrimeQ]}]==DivisorSigma[1, #+1]-(#+1)&]

CROSSREFS

Cf. A000668, A001065, A008472, A006145.

#4 by Metin Sariyar at Fri Jul 08 07:09:12 EDT 2022

NAME

allocated for Metin SariyarNumbers k such that sum of distinct primes dividing k equals to the sum of proper divisors of k+1.

DATA

3, 7, 14, 31, 127, 206, 2974, 8191, 19358, 20490, 131071, 147454, 286122, 289650, 292332, 441276, 524287, 909498, 1207358, 1657968, 1782540, 2490042, 3368860, 9274806

OFFSET

1,1

COMMENTS

Numbers k such that A008472(k) = A001065(k+1). All Mersenne primes are terms.

EXAMPLE

Example: 14 is a term because A008472(14) = 2+7 = A001065(15) = 1+3+5.

MATHEMATICA

Select[Range[19358], Sum[f, {f, Select[Divisors[#], PrimeQ]}]==DivisorSigma[1, #+1]-(#+1)&]

CROSSREFS

Cf. A000668, A001065, A008472.

KEYWORD

allocated

nonn,more

AUTHOR

Metin Sariyar, Jul 08 2022

STATUS

approved

editing

#3 by Metin Sariyar at Fri Jul 08 07:09:12 EDT 2022

NAME

allocated for Metin Sariyar

KEYWORD

recycled

allocated

#2 by David Lovler at Fri Jul 08 01:02:02 EDT 2022

NAME

allocated for David Lovler

KEYWORD

allocated

recycled

#1 by David Lovler at Wed Jun 01 01:20:47 EDT 2022

NAME

allocated for David Lovler

KEYWORD

allocated

STATUS

approved