A257105 Composite numbers n such that n'=(n+8)', where n' is the arithmetic derivative of n.

132, 476, 2108, 16748, 27548, 28676, 99524, 100076, 239948, 308228, 344129, 573476, 601676, 822908, 860276, 883268, 1673228, 3274010, 4959476, 7548956, 8916044, 9048428, 9215348, 9643169, 9833588, 10011908, 14773676, 17119436, 18529964, 19459028, 21335948, 21739148

Offset

1,1

Comments

If the limitation of being composite is removed we also have the numbers p such that if p is prime then p + 8 is prime too (A023202).

Links

Table of n, a(n) for n=1..32.

Example

132' = (132 + 8)' = 140' = 188;
476' = (476 + 8)' = 484' = 572.

Maple

with(numtheory); P:= proc(q, h) local a, b, n, p;
for n from 1 to q do if not isprime(n) then a:=n*add(op(2, p)/op(1, p), p=ifactors(n)[2]); b:=(n+h)*add(op(2, p)/op(1, p), p=ifactors(n+h)[2]);
if a=b then print(n); fi; fi; od; end: P(10^9, 8);

Mathematica

a[n_] := If[Abs@ n < 2, 0, n Total[#2/#1 & @@@ FactorInteger[Abs@ n]]];
Select[Range@ 100000, And[CompositeQ@ #, a@# == a[# + 8]] &] (* Michael De Vlieger, Apr 22 2015, after Michael Somos at A003415 *)

Crossrefs

Cf. A003415, A023202, A226779.

Sequence in context: A244103 A248555 A253502 * A204834 A241288 A115132

Adjacent sequences: A257102 A257103 A257104 * A257106 A257107 A257108

Keyword

nonn

Author

Paolo P. Lava, Apr 17 2015

Status

approved