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

Author

Antti Karttunen, Jun 13 2018

Keywords

• nonn

Links

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

Crossrefs

Cf. A078898, A078899, A305798, A305799.

Programs

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));

Formula

a(n) = Sum_{d|n} A078898(d)*A078899(n/d).