A286628 a(n) = exponent of the highest power of A000005(n) (number of divisors of n) dividing A000203(n) (sum of divisors of n), a(1) = 1.

1, 0, 2, 0, 1, 1, 3, 0, 0, 0, 2, 0, 1, 1, 1, 0, 1, 0, 2, 1, 2, 1, 3, 0, 0, 0, 1, 0, 1, 1, 5, 0, 2, 0, 2, 0, 1, 1, 1, 0, 1, 1, 2, 1, 1, 1, 4, 0, 1, 0, 1, 0, 1, 1, 1, 1, 2, 0, 2, 1, 1, 2, 0, 0, 1, 1, 2, 1, 2, 1, 3, 0, 1, 0, 0, 0, 2, 1, 4, 0, 0, 0, 2, 0, 1, 1, 1, 0, 1, 0, 2, 1, 3, 2, 1, 1, 1, 0, 1, 0, 1, 1, 3, 0, 2, 0, 2, 0, 1, 1, 1, 0, 1, 1, 2, 1, 0, 1, 2, 0

Offset

1,3

Comments

a(1) = 1 by convention.

Links

Antti Karttunen, Table of n, a(n) for n = 1..10000

Formula

a(n) = A286561(A000203(n), A000005(n)).

Example

A000005(6) = 4, A000203(6) = 12, 4^1 is the highest power of 4 which divides 12, thus a(6) = 1.
A000005(7) = 2, A000203(7) = 8, 2^3 is the highest power of 2 which divides 8, thus a(7) = 3.
A000005(8) = 4, A000203(8) = 15, 4^0 = 1 is the highest power of 4 which divides 15, thus a(8) = 0.

Prog

(PARI) A286628(n) = if(1==n, n, valuation(sigma(n), numdiv(n)));

Crossrefs

Cf. A000005, A000203, A051281, A054025, A286561, A286627.

Cf. A049642 (positions of zeros), A003601 (of nonzeros).

Sequence in context: A321196 A104578 A316827 * A378087 A180243 A326728

Adjacent sequences: A286625 A286626 A286627 * A286629 A286630 A286631

Keyword

nonn

Author

Antti Karttunen, Jun 30 2017

Status

approved