A278254 Least number with the prime signature of n^2; square of the least number with the prime signature of n.

1, 4, 4, 16, 4, 36, 4, 64, 16, 36, 4, 144, 4, 36, 36, 256, 4, 144, 4, 144, 36, 36, 4, 576, 16, 36, 64, 144, 4, 900, 4, 1024, 36, 36, 36, 1296, 4, 36, 36, 576, 4, 900, 4, 144, 144, 36, 4, 2304, 16, 144, 36, 144, 4, 576, 36, 576, 36, 36, 4, 3600, 4, 36, 144, 4096, 36, 900, 4, 144, 36, 900, 4, 5184, 4, 36, 144, 144, 36, 900, 4, 2304, 256, 36, 4, 3600, 36, 36, 36

Offset

1,2

Links

Antti Karttunen, Table of n, a(n) for n = 1..10000

Formula

a(n) = A046523(n^2) = A046523(n)^2.

a(n) = A278259(2*n).

Mathematica

Table[Times @@ MapIndexed[(Prime@ First@ #2)^#1 &, #] &@ If[Length@ # == 1 && #[[1, 1]] == 1, {0}, Reverse@ Sort@ #[[All, -1]]] &@ FactorInteger[ n^2], {n, 120}] (* Michael De Vlieger, Nov 21 2016 *)

Prog

(Scheme)
(define (A278254 n) (A000290 (A046523 n)))
(define (A278254 n) (A046523 (A000290 n)))
(PARI) a(n)=my(f=vecsort(factor(n)[, 2], , 4), p); prod(i=1, #f, (p=nextprime(p+1))^f[i])^2 \\ Charles R Greathouse IV, Feb 03 2017

Crossrefs

Bisection of A278259.

Cf. A000290, A046523, A278238, A278253, A278160, A278162.

Sequence in context: A217954 A273749 A273563 * A091278 A127473 A289625

Adjacent sequences: A278251 A278252 A278253 * A278255 A278256 A278257

Keyword

nonn

Author

Antti Karttunen, Nov 19 2016

Status

approved