A341611 Nonabundant numbers that are not primitive terms of A246282.

8, 16, 27, 28, 32, 44, 45, 50, 52, 63, 64, 68, 75, 76, 81, 92, 98, 99, 105, 110, 116, 117, 124, 128, 130, 135, 136, 147, 148, 152, 153, 154, 164, 165, 170, 171, 172, 175, 182, 184, 188, 189, 190, 195, 207, 212, 225, 230, 231, 232, 236, 238, 243, 244, 245, 248, 250, 255, 256, 261, 266, 268, 273, 279, 284, 285, 290, 292, 296, 297

Offset

1,1

Comments

Terms k of A263837 for which A337345(k) > 1 (or equally, for which A337346(k) > 0).

Numbers k such that sigma(k) <= 2k and k has at least two distinct divisors d such that 2d < A003961(d). By necessity, one of these divisors is then k itself.

If there exists any odd perfect numbers, they must reside in this sequence, because the intersection of A023196 and A337372 is equal to {6}. See the comments in the latter sequence. - Antti Karttunen, Sep 06 2025

Links

Antti Karttunen, Table of n, a(n) for n = 1..20000

Index entries for sequences related to prime indices in the factorization of n.

Index entries for sequences related to sigma(n).

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

Prog

(PARI)
A003961(n) = { my(f = factor(n)); for (i=1, #f~, f[i, 1] = nextprime(f[i, 1]+1)); factorback(f); };
A337345(n) = sumdiv(n, d, A003961(d)>(d+d));
isA341611(n) = ((sigma(n)<=(2*n))&&(1<A337345(n)));

Crossrefs

Intersection of A341610 and A263837. Subsequence of A341614.

Cf. A000203, A003961, A023196, A337345, A337346, A337372.

Sequence in context: A302537 A074750 A190519 * A083419 A329134 A090081

Adjacent sequences: A341608 A341609 A341610 * A341612 A341613 A341614

Keyword

nonn

Author

Antti Karttunen, Feb 22 2021

Status

approved