A343217 Numbers k such that A003415(sigma(k)) >= k, where A003415(x) gives the arithmetic derivative of x.

3, 5, 6, 7, 8, 10, 11, 12, 14, 15, 17, 19, 20, 21, 22, 23, 24, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60, 62, 63, 65, 66, 67, 68, 69, 70, 71, 72, 74, 75, 76, 77, 78, 79, 80, 82, 83, 84, 85, 86, 87, 88, 89, 90, 91, 92, 93, 94, 95, 96, 98, 99

Offset: 1

Author

Antti Karttunen, Apr 08 2021

Keywords

• nonn
• changed

Links

• Antti Karttunen, Table of n, a(n) for n = 1..10000
• Index entries for sequences related to sigma(n)

Crossrefs

Cf. A000203, A003415, A342925, A343216 (complement).

Disjoint union of A342021 and A343218.

Positions of nonnegative terms in A342926.

Programs

Mathematica

Select[Range[100], If[#2 < 2, 0, #2 Total[#2/#1 & @@@ FactorInteger[#2]]] >= #1 & @@ {#, DivisorSigma[1, #]} &] (* Michael De Vlieger, Apr 08 2021 *)

PARI

A003415(n) = if(n<=1, 0, my(f=factor(n)); n*sum(i=1, #f~, f[i, 2]/f[i, 1]));
isA343217(n) = (A003415(sigma(n))>=n);