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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 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

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Last modified June 14 21:27 EDT 2021. Contains 345041 sequences. (Running on oeis4.)