A305799 Dirichlet convolution of A078899 with itself.

1, 2, 2, 5, 2, 6, 2, 10, 7, 6, 2, 16, 2, 6, 8, 18, 2, 20, 2, 16, 8, 6, 2, 34, 11, 6, 20, 16, 2, 26, 2, 30, 8, 6, 12, 50, 2, 6, 8, 36, 2, 26, 2, 16, 28, 6, 2, 66, 15, 32, 8, 16, 2, 56, 12, 38, 8, 6, 2, 68, 2, 6, 30, 47, 12, 26, 2, 16, 8, 38, 2, 104, 2, 6, 38, 16, 16, 26, 2, 74, 47, 6, 2, 70, 12, 6, 8, 38, 2, 88, 16, 16, 8, 6, 12, 118, 2, 42

Offset

1,2

Links

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

Formula

a(n) = Sum_{d|n} A078899(d)*A078899(n/d).

Prog

(PARI)
up_to = 65537;
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];
A305799(n) = sumdiv(n, d, A078899(d)*A078899(n/d));

Crossrefs

Cf. A078899, A305797, A305798.

Sequence in context: A305791 A299764 A301830 * A294339 A185291 A018216

Adjacent sequences: A305796 A305797 A305798 * A305800 A305801 A305802

Keyword

nonn

Author

Antti Karttunen, Jun 13 2018

Status

approved