|
%I #10 Apr 11 2020 05:36:39
%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
|
