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%I #34 Mar 03 2020 19:09:18
%S 31,121,781,2801,16105,30941,88741,137561,292561,732541,954305,
%T 1926221,2896405,3500201,4985761,8042221,12326281,14076605,20456441,
%U 25774705,28792661,39449441,48037081,63455221,89451461,105101005,113654321
%N a(n) = 1 + prime(n) + prime(n)^2 + prime(n)^3 + prime(n)^4.
%C Thébault shows that a(2) = 121 is the only square in this sequence. - _Charles R Greathouse IV_, Jul 23 2013
%C Giovanni Resta has found that 28792661 is the first Sophie Germain prime of this form (and actually of the form p = (n^m-1)/(n-1) for any p-1 > n, m > 1). - _M. F. Hasler_, Mar 03 2020
%D Victor Thébault, Curiosités arithmétiques, Mathesis 62 (1953), pp. 120-129.
%H Ivan Panchenko, <a href="/A131992/b131992.txt">Table of n, a(n) for n = 1..1000</a>
%F a(n) = 1 + A131991(n)*A000040(n).
%F a(n) = (A050997(n) - 1)/A006093(n).
%F a(n) = A000203(prime(n)^4). - _R. J. Mathar_, Mar 15 2018
%F a(n) = (prime(n)^5 - 1)/(prime(n) - 1) = A053699(prime(n)). (This is also meant by the 2nd formula.) - _M. F. Hasler_, Mar 03 2020
%e a(1) = 31 because prime(1) = 2 and 1 + 2 + 2^2 + 2^3 + 2^4 = 1 + 2 + 4 + 8 + 16 = 31.
%t Table[Sum[Prime[n]^k, {k, 0, 4}], {n, 30}] (* _Alonso del Arte_, May 24 2015 *)
%o (PARI) a(n)=sigma(prime(n)^4) \\ _Charles R Greathouse IV_, Jul 23 2013
%Y Cf. A030514, A008864, A060800, A131993.
%Y Equals A053699 restricted to prime indices. Subsequence of primes is A190527.
%K nonn,easy
%O 1,1
%A _Reinhard Zumkeller_, Aug 06 2007
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