A305797 Dirichlet convolution of A078898 with A078899.

1, 2, 2, 5, 2, 7, 2, 11, 6, 9, 2, 19, 2, 11, 8, 23, 2, 24, 2, 25, 9, 15, 2, 45, 8, 17, 17, 31, 2, 39, 2, 47, 11, 21, 10, 66, 2, 23, 12, 62, 2, 48, 2, 43, 27, 27, 2, 100, 10, 48, 14, 49, 2, 76, 11, 79, 15, 33, 2, 113, 2, 35, 32, 95, 12, 66, 2, 61, 17, 69, 2, 161, 2, 41, 37, 67, 12, 75, 2, 142, 44, 45, 2, 142, 13, 47, 20, 111, 2, 143, 13, 79, 21, 51, 14

Offset

1,2

Links

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

Formula

a(n) = Sum_{d|n} A078898(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);
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];
v078899 = ordinal_transform(vector(up_to, n, A006530(n)));
A078899(n) = v078899[n];
A305797(n) = sumdiv(n, d, A078898(d)*A078899(n/d));

Crossrefs

Cf. A078898, A078899, A305798, A305799.

Sequence in context: A359101 A024931 A256612 * A029648 A126103 A316895

Adjacent sequences: A305794 A305795 A305796 * A305798 A305799 A305800

Keyword

nonn

Author

Antti Karttunen, Jun 13 2018

Status

approved