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A097272 Least integer with same "mod 2 prime signature" as n. 5
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 (list; graph; refs; listen; history; text; internal format)
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

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Last modified December 1 05:33 EST 2021. Contains 349426 sequences. (Running on oeis4.)