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A317834 Numerators of rational valued sequence whose Dirichlet convolution with itself yields A078899 (the ordinal transform of A006530, the largest prime factor of n). 5
1, 1, 1, 7, 1, 3, 1, 17, 11, 3, 1, 19, 1, 3, 5, 139, 1, 23, 1, 19, 5, 3, 1, 39, 19, 3, 45, 19, 1, 13, 1, 263, 5, 3, 9, 77, 1, 3, 5, 55, 1, 13, 1, 19, 43, 3, 1, 387, 27, 47, 5, 19, 1, 59, 9, 71, 5, 3, 1, 43, 1, 3, 51, 995, 9, 13, 1, 19, 5, 25, 1, 87, 1, 3, 59, 19, 13, 13, 1, 707, 467, 3, 1, 59, 9, 3, 5, 71, 1, 53, 13, 19, 5, 3, 9, 1069, 1 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,4

COMMENTS

The first negative term is a(216) = -97.

LINKS

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

FORMULA

a(n) = numerator of f(n), where f(1) = 1, f(n) = (1/2) * (A078899(n) - Sum_{d|n, d>1, d<n} f(d) * f(n/d)) for n > 1.

PROG

(PARI)

up_to = 16384;

ordinal_transform(invec) = { my(om = Map(), outvec = vector(length(invec)), pt); for(i=1, length(invec), if(mapisdefined(om, invec[i]), pt = mapget(om, invec[i]), pt = 0); outvec[i] = (1+pt); mapput(om, invec[i], (1+pt))); outvec; };

A006530(n) = if(n>1, vecmax(factor(n)[, 1]), 1);

v078899 = ordinal_transform(vector(up_to, n, A006530(n)));

A078899(n) = v078899[n];

A317834aux(n) = if(1==n, n, (A078899(n)-sumdiv(n, d, if((d>1)&&(d<n), A317834aux(d)*A317834aux(n/d), 0)))/2);

A317834(n) = numerator(A317834aux(n));

CROSSREFS

Cf. A078899, A046644 (denominators).

Cf. also A305799, A317833, A317830.

Sequence in context: A200923 A317830 A317938 * A039616 A201585 A089562

Adjacent sequences:  A317831 A317832 A317833 * A317835 A317836 A317837

KEYWORD

sign,frac

AUTHOR

Antti Karttunen, Aug 12 2018

STATUS

approved

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Last modified April 22 06:14 EDT 2019. Contains 322329 sequences. (Running on oeis4.)