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A130279 Smallest number having exactly n square divisors. 5
1, 4, 16, 36, 256, 144, 4096, 576, 1296, 2304, 1048576, 3600, 16777216, 36864, 20736, 14400, 4294967296, 32400, 68719476736, 57600, 331776, 9437184, 17592186044416, 129600, 1679616, 150994944, 810000, 921600, 72057594037927936 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

A046951(a(n)) = n and A046951(m) <> n for m < a(n);

all terms are smooth squares: if prime(k) is a factor of a(n) then also prime(i) are factors, i<k;

a(p) = 2^(2*(p-1)) for primes p;

if prime(j) is the greatest prime factor of a(n) then a(2*n) = a(n)*prime(j+1)^2;

A001221(a(n)) = A122375(n); A001222(a(n)) = 2*A122376(n).

LINKS

Amiram Eldar, Table of n, a(n) for n = 1..100

Eric Weisstein's World of Mathematics, Smooth Number

PROG

(PARI) a(n) = my(k=1); while(sumdiv(k, d, issquare(d)) != n, k++); k; \\ Michel Marcus, Jul 15 2019

CROSSREFS

Cf. A046951, A001221, A122375, A122376.

Sequence in context: A081456 A223403 A263385 * A030158 A054246 A173545

Adjacent sequences:  A130276 A130277 A130278 * A130280 A130281 A130282

KEYWORD

nonn

AUTHOR

Reinhard Zumkeller, May 20 2007

STATUS

approved

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Last modified April 13 01:36 EDT 2021. Contains 342934 sequences. (Running on oeis4.)