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A353791
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Multiplicative with a(p^e) = ((p-1)*q)^e, where q is the largest prime less than p, and 1 if p = 2.
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4
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1, 1, 4, 1, 12, 4, 30, 1, 16, 12, 70, 4, 132, 30, 48, 1, 208, 16, 306, 12, 120, 70, 418, 4, 144, 132, 64, 30, 644, 48, 870, 1, 280, 208, 360, 16, 1116, 306, 528, 12, 1480, 120, 1722, 70, 192, 418, 1978, 4, 900, 144, 832, 132, 2444, 64, 840, 30, 1224, 644, 3074, 48, 3540, 870, 480, 1, 1584, 280, 4026, 208, 1672, 360
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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} ((p^3-p^2)/(p^3-p*q+q)) = 0.1075035014..., where q(p) = prevprime(p) = A151799(p) if p > 2 and q(2) = 1. - Amiram Eldar, Dec 31 2022
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MATHEMATICA
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f[p_, e_] := (If[p == 2, 1, NextPrime[p, -1]]*(p-1))^e; a[1] = 1; a[n_] := Times @@ f @@@ FactorInteger[n]; Array[a, 70] (* Amiram Eldar, Dec 31 2022 *)
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PROG
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(PARI) A353791(n) = { my(f=factor(n>>valuation(n, 2))); for(i=1, #f~, f[i, 1] = (f[i, 1]-1)*precprime(f[i, 1]-1)); factorback(f); };
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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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