A072663 Numbers m such that Sum_{k=1..m} (-1)^k*k*floor(m/k) = 0.

2, 26, 28, 76, 210, 1801, 3508, 16180, 29286, 33988, 1161208, 4010473, 164048770, 18294479654

Offset: 1

Author

Benoit Cloitre, Aug 10 2002

Keywords

• nonn
• more

Comments

It is easy to see that if f(n) = A024919(n) = Sum_{k=1..n} (-1)^k*k*floor(n/k) then f(n) = f(n-1) + (2^(L+1)-3)*sigma(M) if n=2^L*M, where M is odd and L >= 0. Using this we can get a faster program to calculate this sequence. - Robert Gerbicz, Aug 30 2002

Crossrefs

The zeros of A024919.

Programs

Mathematica

f[n_] := Sum[(-1)^i*i*Floor[n/i], {i, 1, n}]; Do[s = f[n]; If[s == 0, Print[n]], {n, 1, 40000}]

PARI

lista(nn) = {my(s=-1); for(m=2, nn, x=bitand(m, -m); if((s+=(2*x-3)*sigma(m/x)) == 0, print1(m, ", "))); } \\ Jinyuan Wang, Apr 06 2020

Extensions

Four more terms from Klaus Brockhaus, Aug 13 2002

More terms from Robert Gerbicz, Aug 30 2002

a(14) from Giovanni Resta, Apr 06 2020