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A131992 1 + prime(n) + prime(n)^2 + prime(n)^3 + prime(n)^4. 10
31, 121, 781, 2801, 16105, 30941, 88741, 137561, 292561, 732541, 954305, 1926221, 2896405, 3500201, 4985761, 8042221, 12326281, 14076605, 20456441, 25774705, 28792661, 39449441, 48037081, 63455221, 89451461, 105101005, 113654321 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

Thébault shows that a(2) = 121 is the only square in this sequence. - Charles R Greathouse IV, Jul 23 2013

REFERENCES

Victor Thébault, Curiosités arithmétiques, Mathesis 62 (1953), pp. 120-129.

LINKS

Ivan Panchenko, Table of n, a(n) for n = 1..1000

FORMULA

a(n) = 1 + A131991(n)*A000040(n).

a(n) = (A050997(n) - 1)/A006093(n).

EXAMPLE

a(1) = 31 because prime(1) = 2 and 1 + 2 + 2^2 + 2^3 + 2^4 = 1 + 2 + 4 + 8 + 16 = 31.

MATHEMATICA

Table[Sum[Prime[n]^k, {k, 0, 4}], {n, 30}] (* Alonso del Arte, May 24 2015 *)

PROG

(MAGMA) [ 1+NthPrime(n)+NthPrime(n)^2+NthPrime(n)^3+NthPrime(n)^4: n in [1..30] ]; // Vincenzo Librandi, Dec 27 2010

(PARI) a(n)=sigma(prime(n)^4)  \\ Charles R Greathouse IV, Jul 23 2013

CROSSREFS

Cf. A030514, A008864, A060800, A131993.

Sequence in context: A202994 A038992 A068021 * A042884 A153073 A042886

Adjacent sequences:  A131989 A131990 A131991 * A131993 A131994 A131995

KEYWORD

nonn

AUTHOR

Reinhard Zumkeller, Aug 06 2007

STATUS

approved

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Last modified November 19 10:44 EST 2017. Contains 294936 sequences.