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A266890 Squares whose arithmetic derivative is a square. 0
0, 1, 4, 256, 11664, 262144, 531441, 11943936, 156250000, 544195584, 4294967296, 7119140625, 24794911296, 160000000000, 195689447424, 1129718145924, 7290000000000, 8916100448256, 10851569165584, 95367431640625, 332150625000000, 406239826673664, 494424620106921 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,3

COMMENTS

Sequence is infinite since it contains all the numbers of the form 4^(k^2). - Giovanni Resta, May 28 2016

LINKS

Table of n, a(n) for n=1..23.

EXAMPLE

0' = 0 = 0^2; 1' = 0 = 0^2; 4' = 4 = 2^2; 256' = 1024 = 32^2; 11664' = 46656 = 216^2.

MAPLE

with(numtheory): P:=proc(q) local a, n, p;

for n from 0 to q do a:=n^2*add(op(2, p)/op(1, p), p=ifactors(n^2)[2]);

if trunc(sqrt(a))*trunc(sqrt(a))=a then print(n^2);  fi;

od; end: P(10^9);

PROG

(PARI) ad(n) = if (n<1, 0, my(f = factor(n)); n*sum(k=1, #f~, f[k, 2]/f[k, 1]));

lista(nn) = {for (n=0, nn, if (issquare(ad(n^2)), print1(n^2, ", ")); ); } \\ Michel Marcus, Apr 08 2016

CROSSREFS

Cf. A003415, A008848.

Sequence in context: A063073 A093760 A062075 * A013734 A209588 A085534

Adjacent sequences:  A266887 A266888 A266889 * A266891 A266892 A266893

KEYWORD

nonn

AUTHOR

Paolo P. Lava, Apr 08 2016

EXTENSIONS

a(17)-a(23) from Giovanni Resta, May 28 2016

STATUS

approved

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Last modified September 22 00:42 EDT 2020. Contains 337276 sequences. (Running on oeis4.)