A387721 - OEIS

%I #14 Sep 07 2025 21:54:35

%S 6,10,12,14,15,18,20,21,22,24,26,28,30,34,36,38,40,42,44,45,46,48,50,

%T 52,54,56,58,60,62,66,68,70,72,74,75,76,78,80,82,84,86,88,90,92,94,96,

%U 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

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

%C 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.

%H Antti Karttunen, <a href="/A387721/b387721.txt">Table of n, a(n) for n = 1..10000</a>

%o (PARI)

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

%o is_A387721(n) = (A107758(n)>(2*n));

%Y Cf. A107758.

%Y Complement of (A052396 U A387720).

%Y Disjoint union of A387722 and A387723.

%Y Positions of positive terms in A387725.

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

%K nonn

%O 1,1

%A _Antti Karttunen_, Sep 06 2025