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A113957 Sum of the divisors of n which are not divisible by 7. 13
1, 3, 4, 7, 6, 12, 1, 15, 13, 18, 12, 28, 14, 3, 24, 31, 18, 39, 20, 42, 4, 36, 24, 60, 31, 42, 40, 7, 30, 72, 32, 63, 48, 54, 6, 91, 38, 60, 56, 90, 42, 12, 44, 84, 78, 72, 48, 124, 1, 93, 72, 98, 54, 120, 72, 15, 80, 90, 60, 168, 62, 96, 13, 127, 84, 144, 68, 126, 96, 18, 72 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

REFERENCES

B. C. Berndt, Ramanujan's Notebooks Part III, Springer-Verlag, see p. 467, Entry 5(i).

LINKS

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

FORMULA

a(n) is multiplicative and a(p^e) = 1, if p=7, a(p^e) = (p^(e+1)-1)/(p-1) otherwise.

G.f.: ((theta_3(z)*theta_3(7z) + theta_2(z)*theta_2(7z))^2-1)/4.

L.g.f.: log(Product_{k>=1} (1 - x^(7*k))/(1 - x^k)) = Sum_{n>=1} a(n)*x^n/n. - Ilya Gutkovskiy, Mar 14 2018

PROG

(PARI) a(n)=if(n<1, 0, sigma(n/7^valuation(n, 7)))

CROSSREFS

Cf. A028594(n)=4*a(n) if n>0.

Cf. A244600.

Sequence in context: A057032 A279388 A292288 * A073185 A284341 A073183

Adjacent sequences:  A113954 A113955 A113956 * A113958 A113959 A113960

KEYWORD

nonn,mult

AUTHOR

Michael Somos, Nov 10 2005

STATUS

approved

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Last modified August 18 04:50 EDT 2019. Contains 326072 sequences. (Running on oeis4.)