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

1,1

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

Links

Table of n, a(n) for n=1..14.

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}]

Prog

(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

Crossrefs

The zeros of A024919.

Sequence in context: A278479 A351921 A022375 * A276176 A050905 A067571

Adjacent sequences: A072660 A072661 A072662 * A072664 A072665 A072666

Keyword

nonn,more

Author

Benoit Cloitre, Aug 10 2002

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

Status

approved