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

1,1

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

Links

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

Example

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

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 *)

Crossrefs

Cf. A003415, A023200, A226779.

Sequence in context: A189004 A183310 A280884 * A146560 A174969 A176069

Adjacent sequences: A257100 A257101 A257102 * A257104 A257105 A257106

Keyword

nonn

Author

Paolo P. Lava, Apr 17 2015

Extensions

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

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

Status

approved