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A120289
Primes p such that p divides the numerator of Sum_{k=1..n-1} 1/prime(k)^p, where p = prime(n).
2
5, 19, 47, 79, 109
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OFFSET
1,1
COMMENTS
Next term > 1690. -
Michael S. Branicky
, Jun 27 2022
LINKS
Table of n, a(n) for n=1..5.
EXAMPLE
a(1) = 5 because prime 5 divides 275 = numerator(1/2^5 + 1/3^5).
Sum_{k=1..n-1} 1/prime(k)^prime(n) begins:
n=2: 1/2^3 = 1/8;
n=3: 1/2^5 + 1/3^5 = 275/7776;
n=4: 1/2^7 + 1/3^7 + 1/5^7 = 181139311/21870000000;
n=5: 1/2^11 + 1/3^11 + 1/5^11 + 1/7^11 = 17301861338484245234233/35027750054222100000000000.
PROG
(Python)
from fractions import Fraction
from sympy import isprime, primerange
def ok(p):
if p < 3 or not isprime(p): return False
s = sum(Fraction(1, pk**p) for pk in primerange(2, p))
return s.numerator%p == 0
print([k for k in range(200) if ok(k)]) #
Michael S. Branicky
, Jun 26 2022
CROSSREFS
Cf.
A119722
.
Sequence in context:
A146736
A176358
A045458
*
A243895
A024191
A277801
Adjacent sequences:
A120286
A120287
A120288
*
A120290
A120291
A120292
KEYWORD
nonn
AUTHOR
Alexander Adamchuk
, Jul 08 2006
STATUS
approved
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Last modified September 12 22:20 EDT 2024. Contains 375855 sequences. (Running on oeis4.)