A163822 Number of divisors d of 2n such that gcd(d-1,2n/d-1) = 1.

2, 1, 2, 2, 2, 4, 2, 2, 4, 4, 2, 6, 2, 2, 6, 4, 2, 6, 2, 4, 6, 4, 2, 8, 4, 2, 6, 6, 2, 10, 2, 2, 4, 4, 4, 10, 2, 2, 6, 8, 2, 10, 2, 4, 10, 4, 2, 8, 4, 4, 6, 6, 2, 10, 6, 4, 6, 4, 2, 12, 2, 2, 8, 6, 4, 10, 2, 4, 6, 10, 2, 12, 2, 2, 10, 6, 4, 8, 2, 6, 8, 4, 2, 14, 6, 2, 6, 4, 2, 16, 6, 4, 4, 4, 4, 12, 2, 2, 10

Offset

1,1

Comments

The corresponding values for odd n are all zero, since then 2 is a common divisor of (d-1,n/d-1).

Links

Antti Karttunen, Table of n, a(n) for n = 1..10080

Antti Karttunen, Data supplement: n, a(n) computed for n = 1..65537

Mathematica

a[n_] := DivisorSum[2*n, 1 &, CoprimeQ[#-1, 2*n/#-1] &]; Array[a, 100] (* Amiram Eldar, Apr 23 2024 *)

Prog

(PARI) a(n)=local(d, r); r=0; d=divisors(2*n); for(k=1, #d, if(gcd(d[k]-1, 2*n\d[k]-1)==1, r++)); r

Crossrefs

Cf. A000005, A163823.

Sequence in context: A079526 A353339 A291708 * A029203 A363526 A159805

Adjacent sequences: A163819 A163820 A163821 * A163823 A163824 A163825

Keyword

nonn

Author

Franklin T. Adams-Watters, Aug 04 2009

Status

approved