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A257107 Composite numbers n such that n'=(n+12)', where n' is the arithmetic derivative of n. 0
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 (list; graph; refs; listen; history; text; internal format)
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

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Last modified September 29 20:22 EDT 2020. Contains 337432 sequences. (Running on oeis4.)