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A116073 Sum of the divisors of n that are not divisible by 5. 15
1, 3, 4, 7, 1, 12, 8, 15, 13, 3, 12, 28, 14, 24, 4, 31, 18, 39, 20, 7, 32, 36, 24, 60, 1, 42, 40, 56, 30, 12, 32, 63, 48, 54, 8, 91, 38, 60, 56, 15, 42, 96, 44, 84, 13, 72, 48, 124, 57, 3, 72, 98, 54, 120, 12, 120, 80, 90, 60, 28, 62, 96, 104, 127, 14, 144, 68, 126, 96, 24 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

REFERENCES

B. C. Berndt, Ramanujan's Notebooks Part III, Springer-Verlag, see p. 463 Entry 4(i).

LINKS

Seiichi Manyama, Table of n, a(n) for n = 1..10000

FORMULA

a(n) is multiplicative with a(5^e) = 1, a(p^e) = (p^(e+1)-1)/(p-1) otherwise.

G.f.: Sum_{k>0} k*x^k/(1-x^k) - 5*k*x^(5*k)/(1-x^(5*k)).

L.g.f.: log(Product_{k>=1} (1 - x^(5*k))/(1 - x^k)) = Sum_{n>=1} a(n)*x^n/n. - Ilya Gutkovskiy, Mar 14 2018

MATHEMATICA

f[p_, e_] := If[p == 5, 1, (p^(e+1)-1)/(p-1)]; a[1] = 1; a[n_] := Times @@ f @@@ FactorInteger[n]; Array[a, 100] (* Amiram Eldar, Sep 17 2020 *)

PROG

(PARI) a(n) = if(n<1, 0, sumdiv(n, d, (d%5>0)*d))

CROSSREFS

Cf. A028887(n) = 6*a(n) if n>0.

Cf. A145466.

Cf. A035207 (number of divisors of n that are not divisible by 5).

Sequence in context: A093087 A130893 A072079 * A166043 A294896 A021292

Adjacent sequences:  A116070 A116071 A116072 * A116074 A116075 A116076

KEYWORD

nonn,mult

AUTHOR

Michael Somos, Feb 04 2006

STATUS

approved

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Last modified March 2 12:26 EST 2021. Contains 341750 sequences. (Running on oeis4.)