cp's OEIS Frontend

A120289 Primes p such that p divides the numerator of Sum_{k=1..n-1} 1/prime(k)^p, where p = prime(n).

%I A120289 #12 Jun 28 2022 15:28:01
%S A120289 5,19,47,79,109
%N A120289 Primes p such that p divides the numerator of Sum_{k=1..n-1} 1/prime(k)^p, where p = prime(n).
%C A120289 Next term > 1690. - _Michael S. Branicky_, Jun 27 2022
%e A120289 a(1) = 5 because prime 5 divides 275 = numerator(1/2^5 + 1/3^5).
%e A120289 Sum_{k=1..n-1} 1/prime(k)^prime(n) begins:
%e A120289   n=2: 1/2^3 = 1/8;
%e A120289   n=3: 1/2^5 + 1/3^5 = 275/7776;
%e A120289   n=4: 1/2^7 + 1/3^7 + 1/5^7 = 181139311/21870000000;
%e A120289   n=5: 1/2^11 + 1/3^11 + 1/5^11 + 1/7^11 = 17301861338484245234233/35027750054222100000000000.
%o A120289 (Python)
%o A120289 from fractions import Fraction
%o A120289 from sympy import isprime, primerange
%o A120289 def ok(p):
%o A120289     if p < 3 or not isprime(p): return False
%o A120289     s = sum(Fraction(1, pk**p) for pk in primerange(2, p))
%o A120289     return s.numerator%p == 0
%o A120289 print([k for k in range(200) if ok(k)]) # _Michael S. Branicky_, Jun 26 2022
%Y A120289 Cf. A119722.
%K A120289 nonn
%O A120289 1,1
%A A120289 _Alexander Adamchuk_, Jul 08 2006