A125907
Numbers k such that k divides 2^4 + 3^4 + 5^4 + ... + prime(k)^4.
Original entry on oeis.org
1, 2951, 38266951, 3053263643573, 3798632877308897
Offset: 1
Cf.
A085450 = smallest m > 1 such that m divides Sum_{k=1..m} prime(k)^n.
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a(1) = 1; s = 2^4; Do[s = s + Prime[2n]^4+Prime[2n+1]^4; If[ Mod[s, 2n+1] == 0, Print[2n+1]], {n,1, 20000000}]
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s=0; n=0; forprime(p=2, 4e9, s+=p^4; if(s%n++==0, print1(n", "))) \\ Charles R Greathouse IV, Mar 21 2011
A341689
a(n) is the sum of the 4th power of the first A125907(n) primes.
Original entry on oeis.org
16, 282090779141153551270, 2210712955689035458600206881540015387708550, 48675866046797839528447895106845001955284425583991669795082795118772, 340116502128393540096171523813533871084766138971398067752157768889198596930173282496
Offset: 1
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sum = 0
for n in range(1,10000000000001):
sum += pow(prime[n],4)
if sum % n == 0:
print(n, prime[n], sum, (sum // n))
A341690
Integer averages of first n primes to the 4th power for some n (A341689(n)/A125907(n)).
Original entry on oeis.org
16, 95591589000729770, 57770815231373815452404527382911050, 15942241394469365582203327807497328235663420076612273764, 89536555153849358635668155008982165719026544119306300984594045157568
Offset: 1
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sum = 0
for n in range(1, 10000000000001):
sum += pow(prime[n], 4)
if sum % n == 0:
print(n, prime[n], sum, (sum // n))
Showing 1-3 of 3 results.
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