A337381 - OEIS

6, 8, 9, 12, 14, 15, 16, 18, 20, 21, 24, 27, 28, 30, 32, 35, 36, 40, 42, 44, 45, 48, 49, 50, 52, 54, 56, 60, 63, 64, 66, 68, 70, 72, 75, 76, 78, 80, 81, 84, 88, 90, 92, 96, 98, 99, 100, 102, 104, 105, 108, 110, 112, 114, 117, 120, 124, 125, 126, 128, 130, 132, 135, 136, 138, 140, 144, 147, 148, 150, 152, 153, 154

COMMENTS

Like the abundancy index (ratio A000203(n)/n), and ratio A003961(n)/n, the ratio A003973(n)/sigma(n) is also multiplicative and > 1 for all n > 1. Thus if the number has a proper divisor that is in this sequence, then the number itself is also. See A337543 for those terms included here, but which have no proper divisor in this sequence. - Antti Karttunen, Aug 31 2020

PROG

(PARI)

A003973(n) = { my(f = factor(n)); for(i=1, #f~, f[i, 1] = nextprime(f[i, 1]+1)); sigma(factorback(f)); };

isA337381(n) = (A003973(n)>=2*sigma(n));

CROSSREFS

Cf. A337382 (complement), A337383 (characteristic function).