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A326297
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If n = Product (p_j^k_j) then a(n) = Product ((p_j - 1)^(k_j - 1)).
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7
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1, 1, 1, 1, 1, 1, 1, 1, 2, 1, 1, 1, 1, 1, 1, 1, 1, 2, 1, 1, 1, 1, 1, 1, 4, 1, 4, 1, 1, 1, 1, 1, 1, 1, 1, 2, 1, 1, 1, 1, 1, 1, 1, 1, 2, 1, 1, 1, 6, 4, 1, 1, 1, 4, 1, 1, 1, 1, 1, 1, 1, 1, 2, 1, 1, 1, 1, 1, 1, 1, 1, 2, 1, 1, 4, 1, 1, 1, 1, 1, 8, 1, 1, 1, 1, 1, 1, 1, 1, 2, 1, 1, 1, 1, 1, 1, 1, 6, 2, 4
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OFFSET
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1,9
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LINKS
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FORMULA
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Dirichlet g.f.: Product_{p prime} (1 + 1/(p^s - p + 1)). - Amiram Eldar, Dec 07 2023
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EXAMPLE
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a(98) = a(2 * 7^2) = (2 - 1)^(1 - 1) * (7 - 1)^(2 - 1) = 6.
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MATHEMATICA
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a[n_] := If[n == 1, 1, Times @@ ((#[[1]] - 1)^(#[[2]] - 1) & /@ FactorInteger[n])]; Table[a[n], {n, 1, 100}]
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PROG
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(PARI) a(n) = my(f=factor(n)); for (k=1, #f~, f[k, 1]--; f[k, 2]--); factorback(f); \\ Michel Marcus, Mar 03 2020
(Python)
from math import prod
from sympy import factorint
def a(n): return prod((p-1)**(e-1) for p, e in factorint(n).items())
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CROSSREFS
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Cf. A003557, A003958, A003959, A007947, A023900, A064478, A064549, A122132 (positions of 1's), A125131, A173557, A325126, A327564.
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KEYWORD
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nonn,mult
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AUTHOR
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STATUS
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approved
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