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A317831 Numerators of rational valued sequence f whose Dirichlet convolution with itself yields A000203 (sigma, the sum of divisors). 8
1, 3, 2, 19, 3, 3, 4, 63, 9, 9, 6, 19, 7, 6, 6, 867, 9, 27, 10, 57, 8, 9, 12, 63, 11, 21, 11, 19, 15, 9, 16, 3069, 12, 27, 12, 171, 19, 15, 14, 189, 21, 12, 22, 57, 27, 18, 24, 867, 41, 33, 18, 133, 27, 33, 18, 63, 20, 45, 30, 57, 31, 24, 18, 22199, 21, 18, 34, 171, 24, 18, 36, 567, 37, 57, 22, 95, 24, 21, 40, 2601, 227, 63, 42, 19, 27, 33 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

LINKS

Antti Karttunen, Table of n, a(n) for n = 1..16384

Index entries for sequences related to sigma(n)

FORMULA

a(n) = numerator of f(n), where f(1) = 1, f(n) = (1/2) * (A000203(n) - Sum_{d|n, d>1, d<n} f(d) * f(n/d)) for n > 1.

PROG

(PARI)

A317831perA317832(n) = if(1==n, n, (sigma(n)-sumdiv(n, d, if((d>1)&&(d<n), A317831perA317832(d)*A317831perA317832(n/d), 0)))/2);

A317831(n) = numerator(A317831perA317832(n));

CROSSREFS

Cf. A317832 (gives the denominators).

Cf. also A000203, A299151.

Sequence in context: A006281 A157705 A185447 * A078073 A317927 A075568

Adjacent sequences:  A317828 A317829 A317830 * A317832 A317833 A317834

KEYWORD

nonn,frac

AUTHOR

Antti Karttunen, Aug 10 2018

STATUS

approved

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Last modified August 2 21:30 EDT 2021. Contains 346429 sequences. (Running on oeis4.)