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A333926 The sum of recursive divisors of n. 8

%I

%S 1,3,4,7,6,12,8,11,13,18,12,28,14,24,24,23,18,39,20,42,32,36,24,44,31,

%T 42,31,56,30,72,32,35,48,54,48,91,38,60,56,66,42,96,44,84,78,72,48,92,

%U 57,93,72,98,54,93,72,88,80,90,60,168,62,96,104,79,84,144

%N The sum of recursive divisors of n.

%C The definition of recursive divisors and the number of recursive divisors of n are in A282446.

%C First differs from A051378 at n = 256.

%H Amiram Eldar, <a href="/A333926/b333926.txt">Table of n, a(n) for n = 1..10000</a>

%F Multiplicative with a(p^k) = 1 + Sum_{d recursive divisor of k} p^d.

%F a(n) <= A051378(n) <= A000203(n).

%e The recursive divisors of 8 are 1, 2 and 8, therefore a(8) = 1 + 2 + 8 = 11.

%t recDivQ[n_, 1] = True; recDivQ[n_, d_] := recDivQ[n, d] = Divisible[n, d] && AllTrue[FactorInteger[d], recDivQ[IntegerExponent[n, First[#]], Last[#]] &]; recDivs[n_] := Select[Divisors[n], recDivQ[n, #] &]; f[p_, e_] := 1 + Total[p^recDivs[e]]; a[1] = 1; a[n_] := Times @@ (f @@@ FactorInteger[n]); Array[a, 100]

%Y Cf. A000203, A051378, A282446, A287957, A287958.

%K nonn,mult

%O 1,2

%A _Amiram Eldar_, Apr 10 2020

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Last modified May 12 17:11 EDT 2021. Contains 343829 sequences. (Running on oeis4.)