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Sum of the twelfth powers of the first n primes.
1

%I #18 Jan 02 2023 12:30:50

%S 4096,535537,244676162,14085963363,3152514340084,26450599462565,

%T 609072836692326,2822387755758487,24737012187778808,

%U 378551795393247849,1166214579181797610,7749166585021832891,30312656885388018972,70272287682650595373,186463770791599173614

%N Sum of the twelfth powers of the first n primes.

%H Robert Price, <a href="/A236218/b236218.txt">Table of n, a(n) for n = 1..1000</a>

%H OEIS Wiki, <a href="https://oeis.org/wiki/Sums_of_primes_divisibility_sequences">Sums of powers of primes divisibility sequences</a>

%H V. Shevelev, <a href="http://list.seqfan.eu/oldermail/seqfan/2013-August/011512.html">Asymptotics of sum of the first n primes with a remainder term</a>

%F a(n) = sum(k = 1 .. n, prime(k)^12).

%t Table[Sum[Prime[k]^12, {k, n}], {n, 1000}]

%t Accumulate[Prime[Range[20]]^12] (* _Harvey P. Dale_, Jan 31 2014 *)

%o (PARI) s=[]; for(n=1, 15, s=concat(s, sum(i=1, n, prime(i)^12))); s \\ _Colin Barker_, Jan 20 2014

%Y Cf. A085450 = smallest m > 1 such that m divides Sum_{k=1..m} prime(k)^n.

%Y Cf. A007504, A045345, A171399, A128165, A233523, A050247, A050248.

%Y Cf. A024450, A111441, A217599, A128166, A233862, A217600, A217601.

%Y Partial sums of A030631.

%K nonn,easy

%O 1,1

%A _Robert Price_, Jan 20 2014