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a(n) = Sum_{i=1..n} prime(i)^(i-1), where prime(i) denotes i-th prime number.
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%I #17 Dec 29 2023 10:49:16

%S 1,4,29,372,15013,386306,24523875,918395614,79229380895,

%T 14586375356764,834214662337565,178751836441797978,

%U 22742242136807984059,1741006366419098769302,258407992554086508103671

%N a(n) = Sum_{i=1..n} prime(i)^(i-1), where prime(i) denotes i-th prime number.

%C The primes in this sequence are 29 = 2^0 + 3^1 + 5^2, 15013 = 2^0 + 3^1 + 5^2 + 7^3 + 11^4, 82630...60939 (a 107-digit number) = 2^0 + 3^1 + 5^2 + ... + 211^46, ...

%H G. C. Greubel, <a href="/A135485/b135485.txt">Table of n, a(n) for n = 1..250</a>

%t f[n_] := Sum[Prime[i]^(i - 1), {i, n}]; Array[f, 16] (* _Robert G. Wilson v_, Feb 12 2008 *)

%o (PARI) a(n) = sum(k=1, n, prime(k)^(k-1)); \\ _Michel Marcus_, Oct 15 2016

%Y Cf. A000040, A087480, A135484.

%Y Partial sums of A093360.

%K nonn

%O 1,2

%A _Ctibor O. Zizka_, Feb 07 2008, Feb 17 2008

%E Edited and extended by _Robert G. Wilson v_, Feb 12 2008