A283995 Least number with same prime signature as the n-th divisorial: a(n) = A046523(A007955(n)).

1, 2, 2, 8, 2, 36, 2, 64, 8, 36, 2, 1728, 2, 36, 36, 1024, 2, 1728, 2, 1728, 36, 36, 2, 331776, 8, 36, 64, 1728, 2, 810000, 2, 32768, 36, 36, 36, 10077696, 2, 36, 36, 331776, 2, 810000, 2, 1728, 1728, 36, 2, 254803968, 8, 1728, 36, 1728, 2, 331776, 36, 331776, 36, 36, 2, 46656000000, 2, 36, 1728, 2097152, 36, 810000, 2, 1728, 36, 810000, 2, 139314069504, 2, 36

Offset: 1

Author

Antti Karttunen, Mar 22 2017

Keywords

• nonn

Links

• Antti Karttunen, Table of n, a(n) for n = 1..1025

Crossrefs

Cf. A007955, A046523, A069264, A283990.

Programs

Mathematica

Table[If[n == 1, 1, Times @@ MapIndexed[Prime[First@ #2]^#1 &, FactorInteger[Times @@ Divisors@ n][[All, -1]]]], {n, 74}] (* Michael De Vlieger, Mar 22 2017 *)

PARI

A007955(n) = if(issquare(n, &n), n^numdiv(n^2), n^(numdiv(n)/2)); \\ From Charles R Greathouse IV, Feb 11 2011
A046523(n) = { my(f=vecsort(factor(n)[, 2], , 4), p); prod(i=1, #f, (p=nextprime(p+1))^f[i]); };  \\ From Charles R Greathouse IV, Aug 17 2011
A283995(n) = A046523(A007955(n));

Python

from math import prod, isqrt
from sympy import prime, factorint, divisor_count
def A283995(n): return (lambda n:prod(prime(i+1)**e for i, e in enumerate(sorted(factorint(n).values(), reverse=True))))((isqrt(n) if (c:=divisor_count(n)) & 1 else 1)*n**(c//2)) # Chai Wah Wu, Jun 25 2022

Scheme

(define (A283995 n) (A046523 (A007955 n)))

Formula

a(n) = A046523(A007955(n)).