A387721 Numbers k for which A107758(k) > 2*k, where A107758 is sigma+, multiplicative function with a(p^e) = 1+sigma(p^e).

6, 10, 12, 14, 15, 18, 20, 21, 22, 24, 26, 28, 30, 34, 36, 38, 40, 42, 44, 45, 46, 48, 50, 52, 54, 56, 58, 60, 62, 66, 68, 70, 72, 74, 75, 76, 78, 80, 82, 84, 86, 88, 90, 92, 94, 96, 98, 100, 102, 104, 105, 106, 108, 110, 112, 114, 116, 118, 120, 122, 124, 126, 130, 132, 134, 135, 136, 138, 140, 142, 144, 146, 148

Offset: 1

Author

Antti Karttunen, Sep 06 2025

Keywords

• nonn
• new

Comments

Note that in contrast to analogous sequences like A005101, A246282, A387711, here it is not guaranteed that multiples of any term are also terms. For example, 21 is a term, but 3*21 = 63 is in A052396. Also 15, 45, 75 are in this sequence, but their multiple 225 is in A387720.

Links

• Antti Karttunen, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A107758.

Complement of (A052396 U A387720).

Disjoint union of A387722 and A387723.

Positions of positive terms in A387725.

Cf. also A005101 (subsequence), A246282, A387711.

Programs

PARI

A107758(n) =  { my(f = factor(n)); prod(k=1, #f~, 1+sigma(f[k, 1]^f[k, 2])); };
is_A387721(n) = (A107758(n)>(2*n));