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

0,2

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.

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

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).

Example

For n=19, A007236(19) = 301, thus a(19) = prime(3)*prime(1) = 5*2 = 10.
For n=52, A007236(52) = 2020, thus a(52) = prime(2)*prime(4) = 3*7 = 21.

Prog

(Scheme, with memoization-macro definec)
(definec (A275733 n) (if (zero? n) 1 (* (A275732 n) (A003961 (A275733 (A257684 n))))))

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.

Sequence in context: A240965 A084228 A328571 * A245499 A323642 A193898

Adjacent sequences: A275730 A275731 A275732 * A275734 A275735 A275736

Keyword

nonn

Author

Antti Karttunen, Aug 08 2016

Status

approved