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A318664 Numerators of the sequence whose Dirichlet convolution with itself yields A064664, the inverse permutation of EKG-sequence. 3
1, 1, 5, 1, 5, -1, 7, 3, -1, -1, 10, 3, 14, -1, -7, 5, 33, 59, 37, 9, -10, -1, 43, -1, -1, -1, 181, 13, 57, 89, 61, 15, -29, -1, -45, 31, 67, -1, -41, 1, 37, 129, 81, 11, 301, -1, 89, 21, 1, 26, -97, 10, 50, -93, -47, -5, -109, -1, 107, -33, 115, -1, 411, 15, -43, 201, 64, 33, -127, 56, 67, 181, 69, -1, 283, 35, -31, 255, 151, 7 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,3

LINKS

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

Index entries for sequences related to EKG sequence

FORMULA

a(n) = numerator of f(n), where f(1) = 1, f(n) = (1/2) * (A064664(n) - Sum_{d|n, d>1, d<n} f(d) * f(n/d)) for n > 1.

For n >= 2, a(2*A000040(n)) = -1.

PROG

(PARI)

v064413 = readvec("b064413_upto65539_terms_only.txt"); \\ From b-file of A064413 prepared beforehand.

A064413(n) = v064413[n];

m064664 = Map();

for(n=1, 65539, mapput(m064664, A064413(n), n));

A064664(n) = mapget(m064664, n);

up_to = (2^14);

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}; \\ From A317937.

v318664_65 = DirSqrt(vector(up_to, n, A064664(n)));

A318664(n) = numerator(v318664_65[n]);

A318665(n) = denominator(v318664_65[n]);

CROSSREFS

Cf. A064664, A304526, A304527, A305293, A305294, A318665 (denominators).

Cf. also A317929, A317930.

Sequence in context: A100947 A096940 A141345 * A329031 A264483 A050340

Adjacent sequences:  A318661 A318662 A318663 * A318665 A318666 A318667

KEYWORD

sign,frac

AUTHOR

Antti Karttunen, Sep 01 2018

STATUS

approved

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Last modified January 22 19:47 EST 2020. Contains 331153 sequences. (Running on oeis4.)