A305798 Dirichlet convolution of A078898 with itself.

1, 2, 2, 5, 2, 8, 2, 12, 5, 12, 2, 22, 2, 16, 8, 28, 2, 28, 2, 34, 10, 24, 2, 56, 5, 28, 14, 46, 2, 52, 2, 64, 14, 36, 8, 83, 2, 40, 16, 88, 2, 70, 2, 70, 26, 48, 2, 136, 5, 64, 20, 82, 2, 94, 10, 120, 22, 60, 2, 164, 2, 64, 34, 144, 12, 106, 2, 106, 26, 100, 2, 220, 2, 76, 36, 118, 8, 124, 2, 216, 42, 84, 2, 224, 14, 88, 32, 184, 2, 192, 10

Offset

1,2

Links

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

Formula

a(n) = Sum_{d|n} A078898(d)*A078898(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; };
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];
A305798(n) = sumdiv(n, d, A078898(d)*A078898(n/d));

Crossrefs

Cf. A078898, A305791, A305796, A305797, A305799.

Sequence in context: A309208 A293225 A353851 * A305808 A353858 A347466

Adjacent sequences: A305795 A305796 A305797 * A305799 A305800 A305801

Keyword

nonn

Author

Antti Karttunen, Jun 13 2018

Status

approved