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A257103 Composite numbers n such that n'=(n+4)', where n' is the arithmetic derivative of n.

%I A257103 #18 Mar 16 2019 19:55:33
%S A257103 21,56,1862,2526,1352797,2201422,3206062,34844422,42400318,8586830293,
%T A257103 20967471193,23194695022,43790421673,45041812729,48438881254,
%U A257103 101060544853,177839630854,180939891343,198419358598,305550990673,354694083622,661663823662,785220739279
%N A257103 Composite numbers n such that n'=(n+4)', where n' is the arithmetic derivative of n.
%C A257103 If the limitation of being composite is removed we also have the lesser of cousin prime pairs (A023200).
%C A257103 a(45) > 5*10^13. - _Hiroaki Yamanouchi_, Aug 27 2015
%H A257103 Hiroaki Yamanouchi, <a href="/A257103/b257103.txt">Table of n, a(n) for n = 1..44</a>
%e A257103 21' = (21 + 4)' = 25' = 10;
%e A257103 56' = (56 + 4)' = 60' = 92.
%p A257103 with(numtheory); P:= proc(q,h) local a,b,n,p;
%p A257103 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 A257103 if a=b then print(n); fi; fi; od; end: P(10^9,4);
%t A257103 a[n_] := If[Abs@n < 2, 0, n Total[#2/#1 & @@@ FactorInteger[Abs@ n]]]; Select[Range@ 10000, And[CompositeQ@ #, a@ # == a[# + 4]] &] (* _Michael De Vlieger_, Apr 22 2015, after _Michael Somos_ at A003415 *)
%Y A257103 Cf. A003415, A023200, A226779.
%K A257103 nonn
%O A257103 1,1
%A A257103 _Paolo P. Lava_, Apr 17 2015
%E A257103 a(8)-a(10) from _Lars Blomberg_, May 06 2015
%E A257103 a(11)-a(23) from _Hiroaki Yamanouchi_, Aug 27 2015