A305803 Dirichlet inverse of A078898.

1, -1, -1, -1, -1, -1, -1, -1, -1, -3, -1, 1, -1, -5, -1, -1, -1, -2, -1, 1, -2, -9, -1, 3, -1, -11, -2, 1, -1, 1, -1, -1, -4, -15, -1, 5, -1, -17, -5, 5, -1, 1, -1, 1, -1, -21, -1, 5, -1, -14, -7, 1, -1, -4, -2, 7, -8, -27, -1, 17, -1, -29, -2, -1, -3, 1, -1, 1, -10, -11, -1, 8, -1, -35, -6, 1, -1, 1, -1, 9, -5, -39, -1, 26, -4, -41, -13, 11, -1, 6, -2, 1

Offset: 1

Author

Antti Karttunen, Jun 13 2018

Keywords

• sign

Links

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

Crossrefs

Cf. A078898, A305798, A305804.

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; };
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];
A305803(n) = if(1==n,1,-sumdiv(n,d,if(dA078898(n/d)*A305803(d),0)));

Formula

a(1) = 1; for n > 1, a(n) = -Sum_{d|n, dA078898(n/d)*a(d).