cp's OEIS Frontend

A097272 Least integer with same "mod 2 prime signature" as n.

%I A097272 #13 Jul 23 2024 10:50:50
%S A097272 1,2,3,4,3,6,3,8,9,6,3,12,3,6,15,16,3,18,3,12,15,6,3,24,9,6,27,12,3,
%T A097272 30,3,32,15,6,15,36,3,6,15,24,3,30,3,12,45,6,3,48,9,18,15,12,3,54,15,
%U A097272 24,15,6,3,60,3,6,45,64,15,30,3,12,15,30,3,72,3,6,45,12,15,30,3,48,81,6,3,60
%N A097272 Least integer with same "mod 2 prime signature" as n.
%C A097272 For n = 2^e_0 * p_1^e_1 * ... * p_n^e_n where p_i is odd prime and e_1 >= e_2 >= ... >= e_n, define "mod 2 prime signature" to be ordered prime exponents (e_0,e_1,...,e_n).
%C A097272 Least integer with a given "mod 2 prime signature" is obtained by replacing p_1 with 3, p_2 with 5,..., p_n with n-th odd prime.
%H A097272 Antti Karttunen, <a href="/A097272/b097272.txt">Table of n, a(n) for n = 1..65537</a>
%F A097272 a(n) = A006519(n)*A003961(A046523(A000265(n))). - _Antti Karttunen_, Sep 27 2018
%t A097272 a[n_] := Module[{m = IntegerExponent[n, 2], e}, 2^m * If[n == 2^m, 1, e = FactorInteger[n/2^m][[;; , 2]]; Times @@ (Prime[Range[2, Length[e] + 1]]^ReverseSort[e])]]; Array[a, 100] (* _Amiram Eldar_, Jul 23 2024 *)
%o A097272 (PARI)
%o A097272 A000265(n) = (n/2^valuation(n, 2));
%o A097272 A003961(n) = my(f = factor(n)); for (i=1, #f~, f[i, 1] = nextprime(f[i, 1]+1)); factorback(f); \\ From A003961
%o A097272 A006519(n) = (1<<valuation(n, 2));
%o A097272 A046523(n) = { my(f=vecsort(factor(n)[, 2], , 4), p); prod(i=1, #f, (p=nextprime(p+1))^f[i]); }; \\ From A046523
%o A097272 A097272(n) = A006519(n)*A003961(A046523(A000265(n))); \\ _Antti Karttunen_, Sep 27 2018
%Y A097272 Cf. A046523, A097273, A097274, A097275.
%K A097272 nonn
%O A097272 1,2
%A A097272 _Ray Chandler_, Aug 22 2004
%E A097272 Offset corrected by _Antti Karttunen_, Sep 27 2018