A133944 Sum mu(k), where the sum is over the integers k which are the "non-isolated divisors" of n and mu(k) is the Moebius function (mu(k) = A008683(k)). A positive divisor, k, of n is non-isolated if (k-1) or (k+1) also divides n.

0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, -1, 0, -1, 0, 0, 0, -1, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, -1, 0, 0, 0, -1, 0, -1, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, -1, 0, -1, 0, 0, 0, -1, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, -1, 0, -1, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, -1, 0, -1, 0, 0, 0, 0, 0, -1, 0, 0, 0, -1, 0, -1, 0

Offset

1,132

Links

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

Formula

A133943(n) = -a(n), for n >= 2.

Maple

A133944 := proc(n) local divs, k, i, a ; divs := convert(numtheory[divisors](n), list) ; a := 0 ; for i from 1 to nops(divs) do k := op(i, divs) ; if k-1 in divs or k+1 in divs then a := a+numtheory[mobius](k) ; fi ; od: RETURN(a) ; end: seq(A133944(n), n=1..120) ; # R. J. Mathar, Oct 21 2007

Prog

(PARI) A133944(n) = sumdiv(n, d, (!if((1==d), (n%2), (n%(d-1))&&(n%(d+1))))*moebius(d)); \\ Antti Karttunen, Sep 02 2018

Crossrefs

Cf. A133943.

Sequence in context: A172051 A093958 A044936 * A210455 A294936 A378539

Adjacent sequences: A133941 A133942 A133943 * A133945 A133946 A133947

Keyword

sign

Author

Leroy Quet, Sep 30 2007

Extensions

More terms from R. J. Mathar, Oct 21 2007

Status

approved