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A317833 Numerators of rational valued sequence whose Dirichlet convolution with itself yields A078898 (the ordinal transform of A020639, the smallest prime factor of n). 5
1, 1, 1, 7, 1, 5, 1, 25, 7, 9, 1, 31, 1, 13, 5, 363, 1, 55, 1, 55, 7, 21, 1, 101, 7, 25, 33, 79, 1, 41, 1, 1335, 11, 33, 5, 305, 1, 37, 13, 177, 1, 59, 1, 127, 47, 45, 1, 1371, 7, 175, 17, 151, 1, 309, 7, 253, 19, 57, 1, 187, 1, 61, 67, 9923, 9, 95, 1, 199, 23, 113, 1, 927, 1, 73, 87, 223, 5, 113, 1, 2379, 715, 81, 1, 265, 11 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,4

COMMENTS

The first negative term is a(840) = -445.

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) * (A078898(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; };

A020639(n) = if(n>1, if(n>n=factor(n, 0)[1, 1], n, factor(n)[1, 1]), 1); \\ From A020639

v078898 = ordinal_transform(vector(up_to, n, A020639(n)));

A078898(n) = v078898[n];

A317833aux(n) = if(1==n, n, (A078898(n)-sumdiv(n, d, if((d>1)&&(d<n), A317833aux(d)*A317833aux(n/d), 0)))/2);

A317833(n) = numerator(A317833aux(n));

CROSSREFS

Cf. A046644, A078898.

Cf. also A305798, A305803, A305804, A317830, A317834.

Sequence in context: A225459 A317847 A181722 * A021587 A195496 A065479

Adjacent sequences:  A317830 A317831 A317832 * A317834 A317835 A317836

KEYWORD

sign,frac

AUTHOR

Antti Karttunen, Aug 10 2018

STATUS

approved

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Last modified April 26 09:52 EDT 2019. Contains 322472 sequences. (Running on oeis4.)