OFFSET
1,2
COMMENTS
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).
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
MATHEMATICA
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 *)
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));
CROSSREFS
KEYWORD
nonn
AUTHOR
Ray Chandler, Aug 22 2004
EXTENSIONS
Offset corrected by Antti Karttunen, Sep 27 2018
STATUS
approved