cp's OEIS Frontend

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

%I A257105 #10 Mar 16 2019 19:54:54
%S A257105 132,476,2108,16748,27548,28676,99524,100076,239948,308228,344129,
%T A257105 573476,601676,822908,860276,883268,1673228,3274010,4959476,7548956,
%U A257105 8916044,9048428,9215348,9643169,9833588,10011908,14773676,17119436,18529964,19459028,21335948,21739148
%N A257105 Composite numbers n such that n'=(n+8)', where n' is the arithmetic derivative of n.
%C A257105 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).
%e A257105 132' = (132 + 8)' = 140' = 188;
%e A257105 476' = (476 + 8)' = 484' = 572.
%p A257105 with(numtheory); P:= proc(q,h) local a,b,n,p;
%p A257105 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]);
%p A257105 if a=b then print(n); fi; fi; od; end: P(10^9,8);
%t A257105 a[n_] := If[Abs@ n < 2, 0, n Total[#2/#1 & @@@ FactorInteger[Abs@ n]]];
%t A257105 Select[Range@ 100000, And[CompositeQ@ #, a@# == a[# + 8]] &] (* _Michael De Vlieger_, Apr 22 2015, after _Michael Somos_ at A003415 *)
%Y A257105 Cf. A003415, A023202, A226779.
%K A257105 nonn
%O A257105 1,1
%A A257105 _Paolo P. Lava_, Apr 17 2015