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A257103
Composite numbers n such that n'=(n+4)', where n' is the arithmetic derivative of n.
1
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
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