A351540 Numbers k that have an odd prime factor p such that p^(1+valuation(k,p)) divides sigma(k).

30, 51, 66, 96, 102, 120, 138, 159, 165, 174, 204, 210, 213, 246, 255, 264, 267, 282, 294, 306, 318, 321, 330, 345, 354, 357, 364, 390, 408, 426, 435, 462, 477, 480, 498, 510, 534, 537, 552, 561, 570, 591, 606, 615, 636, 642, 660, 663, 672, 678, 679, 690, 696, 699, 705, 714, 735, 745, 750, 753, 759, 760, 765, 786

Offset

1,1

Links

Table of n, a(n) for n=1..64.

Index entries for sequences related to sigma(n)

Example

30 = 2 * 3 * 5 is present as sigma(30) = 72 = 2^3 * 3^2, and thus there is at least one odd prime factor (in this case 3) such that a higher power of the same prime divides the sum of divisors of the same number.

Mathematica

Select[Range[2, 800], Function[{k, s}, AnyTrue[DeleteCases[FactorInteger[k][[All, 1]], 2], Mod[s, #^(1 + IntegerExponent[k, #])] == 0 &]] @@ {#, DivisorSigma[1, #]} &] (* Michael De Vlieger, Feb 16 2022 *)

Prog

(PARI)
A351539(n) = { my(f=factor(n), s=sigma(n)); sum(k=1, #f~, (f[k, 1]%2)&&(0==(s%(f[k, 1]^(1+f[k, 2]))))); };
isA351540(n) = (A351539(n)>0);

Crossrefs

Positions of nonzero terms in A351539.

Cf. A000203, A351541 (subsequence).

Probably subsequence: A007691 \ (A323653 U A336702).

Cf. also A336353.

Sequence in context: A228097 A075285 A361668 * A039349 A043172 A043952

Adjacent sequences: A351537 A351538 A351539 * A351541 A351542 A351543

Keyword

nonn

Author

Antti Karttunen, Feb 16 2022

Status

approved