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A256706 Numbers whose arithmetic derivative A003415 is a square different from 1. 1
0, 1, 4, 12, 14, 39, 46, 54, 55, 94, 138, 155, 158, 183, 203, 256, 291, 295, 297, 299, 320, 323, 334, 426, 432, 446, 512, 579, 583, 695, 718, 799, 878, 943, 955, 959, 979, 1002, 1029, 1080, 1146, 1191, 1254, 1255, 1269, 1404, 1411, 1454, 1678, 1703, 1920 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,3

COMMENTS

If n' = 1 (<=> n is prime) were not excluded, the sequence would mainly consist of the primes.

LINKS

Alois P. Heinz, Table of n, a(n) for n = 1..1000

FORMULA

Disjoint from sequence A157037 of numbers whose arithmetic derivative is a prime.

MAPLE

b:= n-> n*add(i[2]/i[1], i=ifactors(n)[2]):

a:= proc(n) option remember; local k;

      for k from 1+`if`(n=1, -1, a(n-1)) while

      (p-> p=1 or not issqr(p))(b(k)) do od; k

    end:

seq(a(n), n=1..70);  # Alois P. Heinz, Apr 08 2015

MATHEMATICA

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 *)

PROG

(PARI) is(n)=!isprime(n)&&issquare(A003415(n))

CROSSREFS

Cf. A003415, A157037.

Sequence in context: A123076 A310563 A260257 * A103020 A215011 A024353

Adjacent sequences:  A256703 A256704 A256705 * A256707 A256708 A256709

KEYWORD

nonn

AUTHOR

M. F. Hasler, Apr 08 2015

STATUS

approved

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Last modified November 13 01:32 EST 2018. Contains 317118 sequences. (Running on oeis4.)