A293231 a(n) = Product_{d|n, dA019565(A193231(d)).

1, 2, 2, 12, 2, 36, 2, 120, 6, 60, 2, 5400, 2, 360, 30, 25200, 2, 56700, 2, 21000, 180, 840, 2, 23814000, 10, 504, 630, 50400, 2, 661500, 2, 554400, 420, 132, 300, 392931000, 2, 792, 252, 242550000, 2, 24948000, 2, 2772000, 22050, 1980, 2, 605113740000, 60, 4851000, 66, 3880800, 2, 720373500, 700, 4889808000, 396, 2772, 2, 588305025000, 2, 1848

Offset: 1

Author

Antti Karttunen, Oct 03 2017

Keywords

• nonn
• base

Links

• Antti Karttunen, Table of n, a(n) for n = 1..1024
• Index entries for sequences related to binary expansion of n

Crossrefs

Cf. A019565, A193231, A290090, A293214, A293232 (rgs-version of this sequence).

Cf. also A001317, A045544, A053576.

Programs

PARI

A019565(n) = {my(j,v); factorback(Mat(vector(if(n, #n=vecextract(binary(n), "-1..1")), j, [prime(j), n[j]])~))}; \\ This function from M. F. Hasler
A193231(n) = { my(x='x); subst(lift(Mod(1, 2)*subst(Pol(binary(n), x), x, 1+x)), x, 2) }; \\ This function from Franklin T. Adams-Watters
A293231(n) = { my(m=1); fordiv(n,d,if(d < n,m *= A019565(A193231(d)))); m; };

Formula

a(n) = Product_{d|n, dA019565(A193231(d)).

For all n >= 1, A007814(a(n)) = A290090(n).

For n = 0..5, a(A001317((2^n)-1)) = A002110((2^n)-1).