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%I #18 Apr 23 2015 11:07:47
%S 0,1,4,12,14,39,46,54,55,94,138,155,158,183,203,256,291,295,297,299,
%T 320,323,334,426,432,446,512,579,583,695,718,799,878,943,955,959,979,
%U 1002,1029,1080,1146,1191,1254,1255,1269,1404,1411,1454,1678,1703,1920
%N Numbers whose arithmetic derivative A003415 is a square different from 1.
%C If n' = 1 (<=> n is prime) were not excluded, the sequence would mainly consist of the primes.
%H Alois P. Heinz, <a href="/A256706/b256706.txt">Table of n, a(n) for n = 1..1000</a>
%F Disjoint from sequence A157037 of numbers whose arithmetic derivative is a prime.
%p b:= n-> n*add(i[2]/i[1], i=ifactors(n)[2]):
%p a:= proc(n) option remember; local k;
%p for k from 1+`if`(n=1, -1, a(n-1)) while
%p (p-> p=1 or not issqr(p))(b(k)) do od; k
%p end:
%p seq(a(n), n=1..70); # _Alois P. Heinz_, Apr 08 2015
%t f[n_] := If[Abs@ n < 2, 0, n Total[#2/#1 & @@@ FactorInteger[Abs@ n]]]; {0}~Join~Flatten@ Position[Array[f, 2000], n_ /; IntegerQ[Sqrt@ n] && n != 1] (* _Michael De Vlieger_, Apr 08 2015, after _Michael Somos_ at A003415 *)
%o (PARI) is(n)=!isprime(n)&&issquare(A003415(n))
%Y Cf. A003415, A157037.
%K nonn
%O 1,3
%A _M. F. Hasler_, Apr 08 2015
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