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A318661 Numerators of the sequence whose Dirichlet convolution with itself yields A055653, sum of phi(d) over all unitary divisors d of n. 3
1, 1, 3, 1, 5, 3, 7, 3, 19, 5, 11, 3, 13, 7, 15, 5, 17, 19, 19, 5, 21, 11, 23, 9, 59, 13, 95, 7, 29, 15, 31, 9, 33, 17, 35, 19, 37, 19, 39, 15, 41, 21, 43, 11, 95, 23, 47, 15, 123, 59, 51, 13, 53, 95, 55, 21, 57, 29, 59, 15, 61, 31, 133, 67, 65, 33, 67, 17, 69, 35, 71, 57, 73, 37, 177, 19, 77, 39, 79, 25, 2019, 41, 83, 21, 85, 43, 87, 33, 89 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,3

LINKS

Antti Karttunen, Table of n, a(n) for n = 1..65537

FORMULA

a(n) = numerator of f(n), where f(1) = 1, f(n) = (1/2) * (A055653(n) - Sum_{d|n, d>1, d<n} f(d) * f(n/d)) for n > 1.

PROG

(PARI)

up_to = 1+(2^16);

A055653(n) = sumdiv(n, d, if(gcd(n/d, d)==1, eulerphi(d))); \\ From A055653

DirSqrt(v) = {my(n=#v, u=vector(n)); u[1]=1; for(n=2, n, u[n]=(v[n]/v[1] - sumdiv(n, d, if(d>1&&d<n, u[d]*u[n/d], 0)))/2); u};

v318661_62 = DirSqrt(vector(up_to, n, A055653(n)));

A318661(n) = numerator(v318661_62[n]);

A318662(n) = denominator(v318661_62[n]);

A318663(n) = valuation(A318662(n), 2);

CROSSREFS

Cf. A055653, A318662 (denominators).

Sequence in context: A318060 A136655 A060819 * A089654 A233526 A097062

Adjacent sequences:  A318658 A318659 A318660 * A318662 A318663 A318664

KEYWORD

nonn

AUTHOR

Antti Karttunen, Sep 03 2018

STATUS

approved

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Last modified January 22 15:57 EST 2019. Contains 319364 sequences. (Running on oeis4.)