A275733 a(0) = 1; for n >= 1, a(n) = A275732(n) * A003961(a(A257684(n))).

1, 2, 3, 6, 3, 6, 5, 10, 15, 30, 15, 30, 5, 10, 15, 30, 15, 30, 5, 10, 15, 30, 15, 30, 7, 14, 21, 42, 21, 42, 35, 70, 105, 210, 105, 210, 35, 70, 105, 210, 105, 210, 35, 70, 105, 210, 105, 210, 7, 14, 21, 42, 21, 42, 35, 70, 105, 210, 105, 210, 35, 70, 105, 210, 105, 210, 35, 70, 105, 210, 105, 210, 7, 14, 21, 42, 21, 42

Offset: 0

Author

Antti Karttunen, Aug 08 2016

Keywords

• nonn
• base

Comments

a(n) = product of primes whose indices are positions of nonzero-digits in factorial base representation of n (see A007623). Here positions are one-based, so that the least significant digit is the position 1, the next least significant the position 2, etc.

Examples

			For n=19, A007623(19) = 301, thus a(19) = prime(3)*prime(1) = 5*2 = 10.
For n=52, A007623(52) = 2020, thus a(52) = prime(2)*prime(4) = 3*7 = 21.
		

Links

• Antti Karttunen, Table of n, a(n) for n = 0..40320
• Indranil Ghosh, Python program for computing this sequence
• Index entries for sequences related to factorial base representation

Crossrefs

Cf. A001221, A002110, A003961, A005117, A007489, A007623, A048675, A060130, A061395, A084558, A257684, A275732.

Subsequence of A005117.

Cf. A275727.

Cf. also A275725, A275734, A275735 for other such prime factorization encodings of A060117/A060118-related polynomials.

Formula

a(0) = 1; for n >= 1, a(n) = A275732(n) * A003961(a(A257684(n))).

Other identities and observations. For all n >= 0:

a(A007489(n)) = A002110(n).

A001221(a(n)) = A001222(a(n)) = A060130(n).

A048675(a(n)) = A275727(n).

A061395(a(n)) = A084558(n).