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A333926 The sum of recursive divisors of n. 8
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, 42, 31, 56, 30, 72, 32, 35, 48, 54, 48, 91, 38, 60, 56, 66, 42, 96, 44, 84, 78, 72, 48, 92, 57, 93, 72, 98, 54, 93, 72, 88, 80, 90, 60, 168, 62, 96, 104, 79, 84, 144 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

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

First differs from A051378 at n = 256.

LINKS

Amiram Eldar, Table of n, a(n) for n = 1..10000

FORMULA

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

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

EXAMPLE

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

MATHEMATICA

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]

CROSSREFS

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

Sequence in context: A284341 A073183 A049418 * A051378 A344575 A254981

Adjacent sequences:  A333923 A333924 A333925 * A333927 A333928 A333929

KEYWORD

nonn,mult

AUTHOR

Amiram Eldar, Apr 10 2020

STATUS

approved

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Last modified June 15 13:25 EDT 2021. Contains 345048 sequences. (Running on oeis4.)