A257107 Composite numbers n such that n'=(n+12)', where n' is the arithmetic derivative of n.

16, 65, 88, 209, 11009, 38009, 680609, 2205209, 2860198, 3515609, 4347209, 5365387, 5809361, 10595009, 12006209, 31979009, 83255059, 89019209, 152915402, 169130009, 172147423, 225869899, 244766009, 247590209, 258084209, 325622009, 357777209, 377330609

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 + 12 is prime too (A046133).

Links

Table of n, a(n) for n=1..28.

Example

16' = (16 + 12)' = 28' = 32;
65' = (65 + 12)' = 77' = 18.

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, 12);

Mathematica

a[n_] := If[Abs@ n < 2, 0, n Total[#2/#1 & @@@ FactorInteger[Abs@ n]]];
Select[Range@ 100000, And[CompositeQ@ #, a@# == a[# + 12]] &] (* Michael De Vlieger, Apr 22 2015, after Michael Somos at A003415 *)

Crossrefs

Cf. A003415, A046133, A226779.

Sequence in context: A031446 A294584 A041492 * A249689 A043402 A044154

Adjacent sequences: A257104 A257105 A257106 * A257108 A257109 A257110

Keyword

nonn

Author

Paolo P. Lava, Apr 17 2015

Extensions

a(16)-a(28) from Lars Blomberg, May 06 2015

Status

approved