A071227 Number of solutions 1<=x<=m to gcd(m,x) = tau(m) where m = A033950(n).

1, 1, 1, 2, 1, 2, 2, 2, 4, 6, 4, 2, 4, 6, 10, 4, 12, 6, 8, 10, 16, 18, 12, 4, 22, 16, 20, 18, 28, 4, 30, 6, 22, 8, 36, 40, 42, 28, 8, 30, 46, 8, 10, 52, 42, 36, 16, 20, 12, 58, 8, 60, 40, 12, 42, 66, 12, 46, 70, 72, 20, 16, 100, 78, 52, 16, 82, 12, 18, 58, 88, 8, 60, 96, 20, 66, 100

Offset: 1

Author

Benoit Cloitre, Jun 10 2002

Keywords

• easy
• nonn

Links

• Amiram Eldar, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A000005 (tau), A033950.

Programs

Mathematica

s[n_] := Module[{d = DivisorSigma[0, n]}, If[Divisible[n, d], Count[Range[n], ?(GCD[n, #] == d &)], Nothing]]; Array[s, 1000] (* _Amiram Eldar, Apr 29 2025 *)

PARI

for(n=1,1000,if(sum(i=1,n,if(gcd(n,i)-numdiv(n),0,1))>0,print1(sum(i=1,n,if(gcd(n,i)-numdiv(n),0,1)),",")))

Extensions

Name corrected by Sean A. Irvine, Jul 05 2024