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A351434
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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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1
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1, 1, 4, 1, 16, 4, 36, 1, 8, 16, 100, 4, 144, 36, 64, 1, 256, 8, 324, 16, 144, 100, 484, 4, 64, 144, 16, 36, 784, 64, 900, 1, 400, 256, 576, 8, 1296, 324, 576, 16, 1600, 144, 1764, 100, 128, 484, 2116, 4, 216, 64, 1024, 144, 2704, 16, 1600, 36, 1296, 784, 3364, 64, 3600, 900, 288, 1, 2304
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OFFSET
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1,3
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LINKS
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FORMULA
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Sum_{k=1..n} a(k) ~ c * n^3, where c = (1/3) * Product_{p prime} (1 - (3*p^2 - 4*p + 2)/(p*(p^3 - p + 1))) = 0.1161464566... . - Amiram Eldar, Nov 19 2022
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MAPLE
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a:= n-> mul((i[1]-1)^(i[2]+1), i=ifactors(n)[2]):
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MATHEMATICA
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f[p_, e_] := (p - 1)^(e + 1); a[1] = 1; a[n_] := Times @@ (f @@@ FactorInteger[n]); Table[a[n], {n, 1, 65}]
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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, Feb 11 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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