A260964 Numbers n such that sigma(n) = (sigma(n)-n)', where sigma(n) is the sum of the divisors of n and (sigma(n)-n)' is the arithmetic derivative of the sum of aliquot parts of n.

24, 492, 2528, 3800, 18416, 526688, 531968, 1084592, 27446468, 1350066372, 2493705728, 7768292812, 15595308928

Offset

1,1

Comments

a(14) > 10^11. - Hiroaki Yamanouchi, Sep 11 2015

Links

Table of n, a(n) for n=1..13.

Example

sigma(24) - 24 = 36 and 36' = 60 = sigma(24);
sigma(492) - 492 = 684 and 684' = 1176 = sigma(492).

Maple

with(numtheory): P:=proc(q) local a, b, c, p, n; for n from 1 to q do
a:=(sigma(n)-n)*add(op(2, p)/op(1, p), p=ifactors((sigma(n)-n))[2]);
if a=sigma(n) then print(n); fi; od; end: P(10^9);

Mathematica

d[0]=d[1]=0; d[n_] := Total[n / Divide@@@ FactorInteger@ n]; Select[Range[10^5], (s = DivisorSigma[1, #]; s == d[s - #]) &] (* Giovanni Resta, Aug 21 2015 *)

Crossrefs

Cf. A000203, A001065, A003415.

Sequence in context: A319426 A275041 A109143 * A186863 A004383 A112390

Adjacent sequences: A260961 A260962 A260963 * A260965 A260966 A260967

Keyword

nonn,more

Author

Paolo P. Lava, Aug 18 2015

Extensions

a(9) from Giovanni Resta, Aug 21 2015

a(10)-a(13) from Hiroaki Yamanouchi, Sep 11 2015

Status

approved