A215935 Number of ordered pairs of primes (p, q) dividing n for which p^e = 1 mod q, where e is the exponent of p in n.

0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 2, 0, 1, 0, 0, 0, 1, 0, 1, 1, 1, 0, 1, 0, 1, 0, 1, 0, 2, 0, 0, 0, 1, 0, 2, 0, 1, 1, 1, 0, 3, 0, 1, 0, 1, 0, 2, 0, 1, 0, 1, 0, 1, 1, 2, 1, 1, 0, 3, 0, 1, 1, 0, 0, 2, 0, 1, 0, 2, 0, 1, 0, 1, 1, 1, 0, 3, 0, 2, 0, 1, 0, 4, 0, 1, 0, 1, 0, 2, 0, 1, 1

Offset: 1

Author

Charles R Greathouse IV, Aug 27 2012

Keywords

• nonn

Comments

If n in A056867 then a(n) = 0.

Examples

			12 is divisible by two primes, 2 and 3. The exponent of 2 is 2 and the exponent of 3 is 1. 2^2 = 1 mod 3 and 3^1 = 1 mod 2, so a(12) = 2.
		

Links

• Alois P. Heinz, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A054395, A056867.

Programs

Maple

a:= proc(n) local l; l:= ifactors(n)[2];
       add(add(`if`(irem(i[1]^i[2], j[1])=1, 1, 0), i=l), j=l)
    end:
seq (a(n), n=1..100);  # Alois P. Heinz, Aug 28 2012

Mathematica

a[n_] := With[{f = FactorInteger[n]}, Sum[ Boole[ Mod[p[[1]]^p[[2]], q[[1]]] == 1], {p, f}, {q, f}]]; Table[a[n], {n, 1, 93}] (* Jean-François Alcover, Sep 03 2012 *)

PARI

a(n)=my(f=factor(n),k=#f~); sum(i=1,k, sum(j=1,k, i!=j && Mod(f[i,1],f[j,1])^f[i,2]==1))