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A237597
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a(n) = |{0 < k < prime(n): n divides pi(k*n)}|, where pi(.) is given by A000720.
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8
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1, 1, 1, 2, 2, 1, 1, 3, 4, 3, 3, 3, 2, 4, 3, 3, 5, 7, 1, 3, 3, 5, 2, 5, 4, 4, 5, 5, 3, 7, 3, 2, 3, 4, 8, 4, 2, 6, 4, 5, 6, 8, 7, 2, 8, 2, 7, 1, 3, 6, 4, 6, 5, 1, 7, 4, 4, 3, 5, 6, 4, 8, 6, 5, 2, 5, 8, 4, 2, 5, 7, 5, 3, 1, 3, 2, 6, 3, 2, 4
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OFFSET
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1,4
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COMMENTS
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Conjecture: a(n) > 0 for all n > 0.
See also A237614 for the least k > 0 with pi(k*n) divisible by n.
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LINKS
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EXAMPLE
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a(6) = 1 since pi(11*6) = 3*6 with 11 < prime(6) = 13.
a(19) = 1 since pi(33*19) = 6*19 with 33 < prime(19) = 67.
a(759) = 1 since pi(2559*759) = 191*759 with 2559 < prime(759) = 5783.
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MATHEMATICA
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a[n_]:=Sum[If[Mod[PrimePi[k*n], n]==0, 1, 0], {k, 1, Prime[n]-1}]
Table[a[n], {n, 1, 80}]
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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