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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).

%I A267143 #31 May 02 2025 18:41:42
%S A267143 5,17,109,257,433,2917,65537,746497,1350001,1769473,3294173,5038849,
%T A267143 5400001,8503057,21600001,28311553,57395629,113246209,145800001,
%U A267143 210827009,984150001,1811939329,2500000001,3936600001,4218750001,5692329217,9331200001,16875000001
%N 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).
%C A267143 Primes from the set {A072873(n) + 1: n>1}.
%C A267143 Fermat primes > 3 from A019434 are in the sequence.
%C A267143 Corresponding values of k: 1, 2, 2, 4, 3, 3, 8, 7, 4, 9, 2, 7, 5, ...
%H A267143 Robert G. Wilson v, <a href="/A267143/b267143.txt">Table of n, a(n) for n = 1..10000</a> (first 185 terms from Jaroslav Krizek)
%e A267143 Prime 433 is a term because 432 = 2^4 * 3^3 and 4/2 + 3/3 = 3 (integer).
%o A267143 (Magma) [n: n in [3..10^8] | IsPrime(n) and Denominator(&+[p[2]/p[1]: p in Factorization(n-1)]) eq 1];
%o A267143 (PARI) isA072873(n)=my(f=factor(n)); for(i=1, #f~, if(f[i, 2]%f[i, 1], return(0))); 1
%o A267143 lista(nn) = {forprime(p=2, nn, if (isA072873(p-1), print1(p, ", ")););} \\ _Michel Marcus_, Jan 21 2016
%Y A267143 Cf. A019434, A072873, A083345, A083346.
%K A267143 nonn
%O A267143 1,1
%A A267143 _Jaroslav Krizek_, Jan 11 2016