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A079579
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Totally multiplicative with p -> (p-1)*p, p prime.
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2
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1, 2, 6, 4, 20, 12, 42, 8, 36, 40, 110, 24, 156, 84, 120, 16, 272, 72, 342, 80, 252, 220, 506, 48, 400, 312, 216, 168, 812, 240, 930, 32, 660, 544, 840, 144, 1332, 684, 936, 160, 1640, 504, 1806, 440, 720, 1012, 2162, 96, 1764, 800, 1632, 624, 2756, 432, 2200, 336
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OFFSET
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1,2
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COMMENTS
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The Dirichlet inverse is 1, -2, -6, 0, -20, 12, -42, 0, 0, 40, -110, 0, -156, 84, 120, 0, -272, ..., i.e., the sequence defined by mu(n)*a(n). - R. J. Mathar, Dec 20 2011
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LINKS
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FORMULA
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a(n) <= n^2.
a(n) = n iff n = 2^k.
Multiplicative sequence with a(p^e) = p^e*(p-1)^e for prime p. - Jaroslav Krizek, Nov 01 2009
Dirichlet g.f.: sum_{n>=1} a(n)/n^s = Product_{primes p} 1/(1+p^(1-s)-p^(2-s)). - R. J. Mathar, Dec 20 2011
Sum_{k=1..n} a(k) ~ c * n^3, where c = zeta(6)/(3*zeta(2)*zeta(3)) = 2*Pi^4/(945*zeta(3)) = A068468 / 3 = 0.171503... .
Sum_{n>=1} 1/a(n) = Product_{p prime} (1 + 1/(p^2-p-1)) (A065488). (End)
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MATHEMATICA
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f[p_, e_] := ((p - 1)*p)^e; a[1] = 1; a[n_] := Times @@ f @@@ FactorInteger[n]; Array[a, 60] (* Amiram Eldar, Oct 23 2022 *)
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PROG
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(Haskell)
a079579 1 = 1
a079579 n = product $ zipWith (*) pfs $ map (subtract 1) pfs
where pfs = a027746_row n
(PARI) a(n) = {my(f = factor(n)); prod(i = 1, #f~, (f[i, 1]*(f[i, 1]-1))^f[i, 2]); } \\ Amiram Eldar, Oct 23 2022
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CROSSREFS
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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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