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A257105 Composite numbers n such that n'=(n+8)', where n' is the arithmetic derivative of n. 0
132, 476, 2108, 16748, 27548, 28676, 99524, 100076, 239948, 308228, 344129, 573476, 601676, 822908, 860276, 883268, 1673228, 3274010, 4959476, 7548956, 8916044, 9048428, 9215348, 9643169, 9833588, 10011908, 14773676, 17119436, 18529964, 19459028, 21335948, 21739148 (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 + 8 is prime too (A023202).

LINKS

Table of n, a(n) for n=1..32.

EXAMPLE

132' = (132 + 8)' = 140' = 188;

476' = (476 + 8)' = 484' = 572.

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, 8);

MATHEMATICA

a[n_] := If[Abs@ n < 2, 0, n Total[#2/#1 & @@@ FactorInteger[Abs@ n]]];

Select[Range@ 100000, And[CompositeQ@ #, a@# == a[# + 8]] &] (* Michael De Vlieger, Apr 22 2015, after Michael Somos at A003415 *)

CROSSREFS

Cf. A003415, A023202, A226779.

Sequence in context: A244103 A248555 A253502 * A204834 A241288 A115132

Adjacent sequences:  A257102 A257103 A257104 * A257106 A257107 A257108

KEYWORD

nonn

AUTHOR

Paolo P. Lava, Apr 17 2015

STATUS

approved

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Last modified October 16 03:15 EDT 2019. Contains 328038 sequences. (Running on oeis4.)