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

21, 56, 1862, 2526, 1352797, 2201422, 3206062, 34844422, 42400318, 8586830293, 20967471193, 23194695022, 43790421673, 45041812729, 48438881254, 101060544853, 177839630854, 180939891343, 198419358598, 305550990673, 354694083622, 661663823662, 785220739279

Offset: 1

Author

Paolo P. Lava, Apr 17 2015

Keywords

• nonn

Comments

If the limitation of being composite is removed we also have the lesser of cousin prime pairs (A023200).

a(45) > 5*10^13. - Hiroaki Yamanouchi, Aug 27 2015

Examples

			21' = (21 + 4)' = 25' = 10;
56' = (56 + 4)' = 60' = 92.
		

Links

• Hiroaki Yamanouchi, Table of n, a(n) for n = 1..44

Crossrefs

Cf. A003415, A023200, A226779.

Programs

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(10^9,4);

Mathematica

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 *)

Extensions

a(8)-a(10) from Lars Blomberg, May 06 2015

a(11)-a(23) from Hiroaki Yamanouchi, Aug 27 2015