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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). 1
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 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

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, ...

LINKS

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

EXAMPLE

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

PROG

(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

CROSSREFS

Cf. A019434, A072873, A083345, A083346.

Sequence in context: A100301 A096178 A084167 * A234797 A062586 A301641

Adjacent sequences:  A267140 A267141 A267142 * A267144 A267145 A267146

KEYWORD

nonn

AUTHOR

Jaroslav Krizek, Jan 11 2016

STATUS

approved

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Last modified October 18 07:58 EDT 2018. Contains 316307 sequences. (Running on oeis4.)