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

%I A283995 #14 Jun 25 2022 21:54:44
%S A283995 1,2,2,8,2,36,2,64,8,36,2,1728,2,36,36,1024,2,1728,2,1728,36,36,2,
%T A283995 331776,8,36,64,1728,2,810000,2,32768,36,36,36,10077696,2,36,36,
%U A283995 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
%N A283995 Least number with same prime signature as the n-th divisorial: a(n) = A046523(A007955(n)).
%H A283995 Antti Karttunen, <a href="/A283995/b283995.txt">Table of n, a(n) for n = 1..1025</a>
%F A283995 a(n) = A046523(A007955(n)).
%t A283995 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 *)
%o A283995 (PARI)
%o A283995 A007955(n) = if(issquare(n, &n), n^numdiv(n^2), n^(numdiv(n)/2)); \\ From _Charles R Greathouse IV_, Feb 11 2011
%o A283995 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
%o A283995 A283995(n) = A046523(A007955(n));
%o A283995 (Scheme) (define (A283995 n) (A046523 (A007955 n)))
%o A283995 (Python)
%o A283995 from math import prod, isqrt
%o A283995 from sympy import prime, factorint, divisor_count
%o A283995 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
%Y A283995 Cf. A007955, A046523, A069264, A283990.
%K A283995 nonn
%O A283995 1,2
%A A283995 _Antti Karttunen_, Mar 22 2017