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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.
3
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
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. A049642 (positions of zeros), A003601 (of nonzeros).
Sequence in context: A321196 A104578 A316827 * A180243 A326728 A330944
KEYWORD
nonn
AUTHOR
Antti Karttunen, Jun 30 2017
STATUS
approved