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 A366146 The sum of divisors of the largest divisor of n that is a cubefull number (A036966). 3
 1, 1, 1, 1, 1, 1, 1, 15, 1, 1, 1, 1, 1, 1, 1, 31, 1, 1, 1, 1, 1, 1, 1, 15, 1, 1, 40, 1, 1, 1, 1, 63, 1, 1, 1, 1, 1, 1, 1, 15, 1, 1, 1, 1, 1, 1, 1, 31, 1, 1, 1, 1, 1, 40, 1, 15, 1, 1, 1, 1, 1, 1, 1, 127, 1, 1, 1, 1, 1, 1, 1, 15, 1, 1, 1, 1, 1, 1, 1, 31, 121, 1 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,8 LINKS Amiram Eldar, Table of n, a(n) for n = 1..10000 FORMULA a(n) = A000203(A360540(n)). a(n) = A000203(n)/A366148(n). a(n) >= 1, with equality if and only if n is cubefree (A004709). a(n) <= A000203(n), with equality if and only if n is cubefull (A036966). Multiplicative with a(p^e) = 1 if e <= 2 and (p^(e+1)-1)/(p-1) otherwise. Dirichlet g.f.: zeta(s-1) * zeta(s) * Product_{p prime} (1 - 1/p^(s-1) + 1/p^(3*s-3) + 1/p^(3*s-2) + 1/p^(3*s-1) - 1/p^(4*s-3) - 1/p^(4*s-2)). MATHEMATICA f[p_, e_] := If[e < 3, 1, (p^(e+1)-1)/(p-1)]; a[1] = 1; a[n_] := Times @@ f @@@ FactorInteger[n]; Array[a, 100] PROG (PARI) a(n) = {my(f = factor(n), p = f[, 1], e = f[, 2]); prod(i = 1, #p, if(e[i] < 3, 1, (p[i]^(e[i]+1)-1)/(p[i]-1)))}; CROSSREFS Cf. A000203, A036966, A295294, A360540, A366076, A366145, A366148. Sequence in context: A333845 A015908 A361355 * A040228 A040229 A318650 Adjacent sequences: A366143 A366144 A366145 * A366147 A366148 A366149 KEYWORD nonn,easy,mult AUTHOR Amiram Eldar, Oct 01 2023 STATUS approved

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Last modified August 15 10:38 EDT 2024. Contains 375173 sequences. (Running on oeis4.)