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A125826
Numbers m that divide 2^7 + 3^7 + 5^7 + ... + prime(m)^7.
2
1, 25, 1677, 21875, 538513, 1015989, 18522325, 1130976595, 1721158369, 561122374231, 1763726985077, 2735295422833, 7631117283951, 22809199833151, 46929434362563, 49217568518075, 151990420653423, 174172511353413, 1258223430425543
OFFSET
1,2
COMMENTS
See A232865 for prime(a(n)). - M. F. Hasler, Dec 01 2013
a(17) > 5.5*10^13. - Bruce Garner, Aug 30 2021
a(18) > 1.56*10^14. - Paul W. Dyson, Mar 02 2022
a(19) > 1.9*10^14. - Bruce Garner, Sep 18 2022
MATHEMATICA
s = 0; Do[s = s + Prime[n]^7; If[ Mod[s, n] == 0, Print[n]], {n, 25000}]
PROG
(PARI) s=0; n=0; forprime(p=2, 4e9, s+=p^7; if(s%n++==0, print1(n", "))) \\ Charles R Greathouse IV, Mar 16 2011
CROSSREFS
Cf. A232865.
Cf. A085450 (smallest m > 1 such that m divides Sum_{k=1..m} prime(k)^n).
Sequence in context: A196299 A196217 A196684 * A263967 A290881 A316911
KEYWORD
hard,nonn
AUTHOR
Alexander Adamchuk, Feb 03 2007
EXTENSIONS
More terms from Ryan Propper, Mar 26 2007
a(8)-a(9) from Charles R Greathouse IV, Mar 16 2011
a(10) from Paul W. Dyson, Jan 05 2021
a(11)-a(12) from Bruce Garner, Feb 26 2021
a(13) from Bruce Garner, Mar 23 2021
a(14) from Bruce Garner, May 19 2021
a(15)-a(16) from Bruce Garner, Aug 30 2021
a(17) from Paul W. Dyson, Mar 02 2022
a(18) from Bruce Garner, Sep 18 2022
a(19) from Paul W. Dyson, Jan 17 2024
STATUS
approved