A328835 Prime shadow of primorial base exp-function: a(n) = A181819(A276086(n)).

1, 2, 2, 4, 3, 6, 2, 4, 4, 8, 6, 12, 3, 6, 6, 12, 9, 18, 5, 10, 10, 20, 15, 30, 7, 14, 14, 28, 21, 42, 2, 4, 4, 8, 6, 12, 4, 8, 8, 16, 12, 24, 6, 12, 12, 24, 18, 36, 10, 20, 20, 40, 30, 60, 14, 28, 28, 56, 42, 84, 3, 6, 6, 12, 9, 18, 6, 12, 12, 24, 18, 36, 9, 18, 18, 36, 27, 54, 15, 30, 30, 60, 45, 90, 21, 42, 42, 84, 63, 126, 5, 10, 10, 20, 15, 30, 10, 20, 20

Offset

0,2

Comments

From Antti Karttunen, Apr 30 2022: (Start)

These are prime-factorization representations of single-variable polynomials where the coefficient of term x^(k-1) (encoded as the exponent of prime(k) in the factorization of n) is equal to the number of times a nonzero digit k occurs in the primorial base representation of n.

Note that this sequence, and all the sequences derived from it as b(n) = f(a(n)), [where f is any integer-valued function] can be represented as b(n) = g(A278226(n)), where g(n) = f(A181819(n)). E.g., if f is the identity function (so that b(n) is this sequence), then g(n) is A181819(n). See the comment and formulas in the latter sequence.

(End)

Links

Antti Karttunen, Table of n, a(n) for n = 0..30030

Index entries for sequences related to primorial numbers

Formula

a(n) = A181819(A276086(n)).

A001222(a(n)) = A267263(n).

A007814(a(n)) = A328614(n).

A061395(a(n)) = A328114(n).

For all n >= 0, a(n) = A181819(A278226(n)) and A181821(a(n)) = A278226(n). - Antti Karttunen, Apr 30 2022

Prog

(PARI)
A181819(n) = factorback(apply(e->prime(e), (factor(n)[, 2])));
A276086(n) = { my(m=1, p=2); while(n, m *= (p^(n%p)); n = n\p; p = nextprime(1+p)); (m); };
A328835(n) = A181819(A276086(n));

Crossrefs

Cf. A001222, A007814, A061395, A181819, A181821, A267263, A276086, A278226 (A286626), A328114, A328614.

Cf. A275735 for analogous sequence.

Sequence in context: A227154 A324655 A275735 * A076435 A257010 A156864

Adjacent sequences: A328832 A328833 A328834 * A328836 A328837 A328838

Keyword

nonn

Author

Antti Karttunen, Oct 29 2019

Status

approved