A344586 Numbers k for which A003415(k) >= A001065(k), where A003415 gives the arithmetic derivative, and A001065 is the sum of proper divisors.

1, 2, 3, 4, 5, 7, 8, 9, 11, 12, 13, 16, 17, 18, 19, 20, 23, 24, 25, 27, 28, 29, 31, 32, 36, 37, 40, 41, 43, 44, 45, 47, 48, 49, 50, 52, 53, 54, 56, 59, 61, 63, 64, 67, 68, 71, 72, 73, 75, 76, 79, 80, 81, 83, 88, 89, 92, 96, 97, 98, 99, 100, 101, 103, 104, 107, 108, 109, 112, 113, 116, 117, 120, 121, 124, 125, 127, 128, 131

Offset: 1

Author

Antti Karttunen, May 24 2021

Keywords

• nonn

Links

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

Crossrefs

Cf. A001065, A003415.

Cf. A212127, A212128 (subsequences), A344585 (complement).

Positions of nonnegative terms in A211991.

Differs from A212165 for the first time at n=121, where a(121) = 220, while A212165(121) = 223.

Programs

PARI

A003415(n) = if(n<=1, 0, my(f=factor(n)); n*sum(i=1, #f~, f[i, 2]/f[i, 1]));
isA344586(n) = (A003415(n) >= (sigma(n)-n));