A305804 Möbius-transform of A078898.

1, 0, 0, 1, 0, 2, 0, 2, 1, 4, 0, 2, 0, 6, 2, 4, 0, 5, 0, 4, 3, 10, 0, 4, 1, 12, 3, 6, 0, 6, 0, 8, 5, 16, 2, 6, 0, 18, 6, 8, 0, 9, 0, 10, 4, 22, 0, 8, 1, 19, 8, 12, 0, 15, 3, 12, 9, 28, 0, 8, 0, 30, 6, 16, 4, 15, 0, 16, 11, 22, 0, 12, 0, 36, 9, 18, 2, 18, 0, 16, 9, 40, 0, 12, 5, 42, 14, 20, 0, 20, 3, 22, 15, 46, 6, 16, 0, 41, 10, 20, 0, 24, 0, 24, 10

Offset

1,6

Links

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

Formula

a(n) = Sum_{d|n} A008683(n/d)*A078898(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];
A305804(n) = sumdiv(n, d, moebius(n/d)*A078898(d));

Crossrefs

Cf. A008683, A078898, A305798, A305803.

Sequence in context: A035573 A361850 A295689 * A053470 A308202 A329152

Adjacent sequences: A305801 A305802 A305803 * A305805 A305806 A305807

Keyword

nonn

Author

Antti Karttunen, Jun 13 2018

Status

approved