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

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, 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, 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

Offset

1,2

Comments

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).

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.

Links

Antti Karttunen, Table of n, a(n) for n = 1..65537

Formula

a(n) = A006519(n)*A003961(A046523(A000265(n))). - Antti Karttunen, Sep 27 2018

Prog

(PARI)
A000265(n) = (n/2^valuation(n, 2));
A003961(n) = my(f = factor(n)); for (i=1, #f~, f[i, 1] = nextprime(f[i, 1]+1)); factorback(f); \\ From A003961
A006519(n) = (1<<valuation(n, 2));
A046523(n) = { my(f=vecsort(factor(n)[, 2], , 4), p); prod(i=1, #f, (p=nextprime(p+1))^f[i]); }; \\ From A046523
A097272(n) = A006519(n)*A003961(A046523(A000265(n))); \\ Antti Karttunen, Sep 27 2018

Crossrefs

Cf. A046523, A097273, A097274, A097275.

Sequence in context: A092089 A117659 A079065 * A126630 A167234 A088043

Adjacent sequences: A097269 A097270 A097271 * A097273 A097274 A097275

Keyword

nonn

Author

Ray Chandler, Aug 22 2004

Extensions

Offset corrected by Antti Karttunen, Sep 27 2018

Status

approved