A293214 a(n) = Product_{d|n, dA019565(d).

1, 2, 2, 6, 2, 36, 2, 30, 12, 60, 2, 2700, 2, 180, 120, 210, 2, 7560, 2, 6300, 360, 252, 2, 661500, 20, 420, 168, 94500, 2, 23814000, 2, 2310, 504, 132, 600, 43659000, 2, 396, 840, 2425500, 2, 187110000, 2, 207900, 352800, 1980, 2, 560290500, 60, 194040, 264, 485100, 2, 115259760, 840, 254677500, 792, 4620, 2, 264737261250000, 2, 13860

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. A001065, A002110, A019565, A048675, A091954, A292257, A293215 (restricted growth sequence transform).

Cf. also A293216, A293221, A293222, A293225, A293231, A293442, A300830, A300831, A300832, A300833, A300834.

Programs

PARI

A019565(n) = {my(j,v); factorback(Mat(vector(if(n, #n=vecextract(binary(n), "-1..1")), j, [prime(j), n[j]])~))}; \\ From A019565
A293214(n) = { my(m=1); fordiv(n,d,if(d < n,m *= A019565(d))); m; };

Formula

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

a(n) = A300830(n) * A300831(n) * A300832(n). - Antti Karttunen, Mar 16 2018

Other identities.

For n >= 0, a(2^n) = A002110(n).

For n >= 1:

A048675(a(n)) = A001065(n).

A001222(a(n)) = A292257(n).

A007814(a(n)) = A091954(n).

A087207(a(n)) = A218403(n).

A248663(a(n)) = A227320(n).