A343216 Numbers k such that A003415(sigma(k)) < k, where A003415(x) gives the arithmetic derivative of x.

1, 2, 4, 9, 13, 16, 18, 25, 36, 37, 49, 50, 61, 64, 73, 81, 97, 100, 101, 109, 113, 121, 137, 144, 157, 169, 173, 181, 193, 225, 229, 241, 242, 256, 257, 277, 281, 289, 313, 317, 324, 325, 333, 337, 353, 361, 373, 397, 400, 401, 409, 421, 433, 441, 457, 484, 512, 529, 541, 549, 576, 577, 578, 601, 613, 617, 625, 641

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, A343217 (complement), A342925.

Positions of negative terms in A342926.

Programs

Mathematica

Select[Range[641], 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]));
isA343216(n) = (A003415(sigma(n))