A332030 a(n) is the product of the distinct positive numbers whose binary digits appear in order, but not necessarily as consecutive digits, in the binary representation of n.

1, 1, 2, 3, 8, 30, 36, 21, 64, 1080, 7200, 2310, 1728, 16380, 3528, 315, 1024, 146880, 9331200, 1580040, 13824000, 1362160800, 170755200, 796950, 331776, 176904000, 2861913600, 72972900, 4741632, 99754200, 1587600, 9765, 32768, 77552640, 86294937600

Offset

0,3

Comments

This sequence is a variant of A165153.

For n > 0, a(n) is the product of the terms of the n-th row of A301983.

Links

Rémy Sigrist, Table of n, a(n) for n = 0..4096

Formula

a(n) >= A165153(n).

a(2^k) = A006125(k+1) for any k >= 0.

a(2^k-1) = A005329(k) for any k >= 0.

Example

For n = 9:
- the binary representation of 9 is "1001",
- the following positive binary strings appear in it: "1", "10", "11", "100", "101" and "1001",
- they correspond to: 1, 2, 3, 4, 5 and 9,
- so a(9) = 1 * 2 * 3 * 4 * 5 * 9 = 1080.

Prog

(PARI) a(n) = my (b=binary(n), s=[0]); for (i=1, #b, s=setunion(s, apply(m -> 2*m+b[i], s))); vecprod(s[2..#s])

Crossrefs

Cf. A005329, A006125, A165153, A301983, A328379 (additive variant).

Sequence in context: A177010 A300484 A004106 * A188498 A012886 A078918

Adjacent sequences: A332027 A332028 A332029 * A332031 A332032 A332033

Keyword

nonn,base

Author

Rémy Sigrist, Feb 05 2020

Status

approved