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%I #8 Sep 27 2018 17:55:00
%S 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 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 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 Least integer with same "mod 2 prime signature" as n.
%C For n = 2^a_0 * p_1^a_1 * ... * p_n^a_n where p_i is odd prime and a_1 >= a_2 >= ... >= a_n, define "mod 2 prime signature" to be ordered prime exponents (a_0,a_1,...,a_n).
%C 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 Antti Karttunen, <a href="/A097272/b097272.txt">Table of n, a(n) for n = 1..65537</a>
%F a(n) = A006519(n)*A003961(A046523(A000265(n))). - _Antti Karttunen_, Sep 27 2018
%o (PARI)
%o A000265(n) = (n/2^valuation(n, 2));
%o A003961(n) = my(f = factor(n)); for (i=1, #f~, f[i, 1] = nextprime(f[i, 1]+1)); factorback(f); \\ From A003961
%o A006519(n) = (1<<valuation(n, 2));
%o A046523(n) = { my(f=vecsort(factor(n)[, 2], , 4), p); prod(i=1, #f, (p=nextprime(p+1))^f[i]); }; \\ From A046523
%o A097272(n) = A006519(n)*A003961(A046523(A000265(n))); \\ _Antti Karttunen_, Sep 27 2018
%Y Cf. A046523, A097273, A097274, A097275.
%K nonn
%O 1,2
%A _Ray Chandler_, Aug 22 2004
%E Offset corrected by _Antti Karttunen_, Sep 27 2018
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