A336353 Numbers k such that sigma(k) does not have any prime factor larger than the largest prime factor of k.

1, 3, 5, 6, 7, 10, 11, 13, 14, 15, 17, 19, 21, 22, 23, 26, 28, 29, 30, 31, 33, 34, 35, 37, 38, 39, 40, 41, 42, 43, 44, 46, 47, 51, 52, 53, 55, 56, 57, 58, 59, 61, 62, 65, 66, 67, 68, 69, 70, 71, 73, 74, 76, 77, 78, 79, 82, 83, 84, 85, 86, 87, 88, 89, 91, 92, 93, 94, 95

Offset

1,2

Comments

Note that the terms after 1 do not form a subsequence of A102750: the first counterexample is 343 = 7^3. See A336354.

Links

Robert Israel, Table of n, a(n) for n = 1..10000

Index entries for sequences where odd perfect numbers must occur, if they exist at all

Maple

filter:= proc(k) uses NumberTheory;
  max(PrimeFactors(sigma(k))) <= max(PrimeFactors(k));
end proc:
select(filter, [$1..100]); # Robert Israel, Dec 29 2025

Mathematica

A336353Q[k_] := FactorInteger[DivisorSigma[1, k]][[-1, 1]] <= FactorInteger[k][[-1, 1]];
Select[Range[100], A336353Q] (* Paolo Xausa, Dec 29 2025 *)

Prog

(PARI) isA336353(n) = !A336352(n);

Crossrefs

Positions of zeros in A336352.

Cf. A102750, A336317.

Subsequences: A000396, A001599, A065091, A105402, A333646 (see comment there), A336354.

Sequence in context: A295307 A073803 A378501 * A182851 A281995 A304452

Adjacent sequences: A336350 A336351 A336352 * A336354 A336355 A336356

Keyword

nonn

Author

Antti Karttunen, Jul 19 2020

Status

approved