A267143 Primes q such that Sum_(q-1; i=1..m) e(i)/p(i) is an integer k, where the prime factorization of n is Product_(n; i=1..m) p(i)^e(i).

5, 17, 109, 257, 433, 2917, 65537, 746497, 1350001, 1769473, 3294173, 5038849, 5400001, 8503057, 21600001, 28311553, 57395629, 113246209, 145800001, 210827009, 984150001, 1811939329, 2500000001, 3936600001, 4218750001, 5692329217, 9331200001, 16875000001

Offset: 1

Author

Jaroslav Krizek, Jan 11 2016

Keywords

• nonn

Comments

Primes from the set {A072873(n) + 1: n>1}.

Fermat primes > 3 from A019434 are in the sequence.

Corresponding values of k: 1, 2, 2, 4, 3, 3, 8, 7, 4, 9, 2, 7, 5, ...

Examples

			Prime 433 is a term because 432 = 2^4 * 3^3 and 4/2 + 3/3 = 3 (integer).
		

Links

• Robert G. Wilson v, Table of n, a(n) for n = 1..10000 (first 185 terms from Jaroslav Krizek)

Crossrefs

Cf. A019434, A072873, A083345, A083346.

Programs

Magma

[n: n in [3..10^8] | IsPrime(n) and Denominator(&+[p[2]/p[1]: p in Factorization(n-1)]) eq 1];

PARI

isA072873(n)=my(f=factor(n)); for(i=1, #f~, if(f[i, 2]%f[i, 1], return(0))); 1
lista(nn) = {forprime(p=2, nn, if (isA072873(p-1), print1(p, ", ")););} \\ Michel Marcus, Jan 21 2016