A319074 a(n) is the sum of the first n nonnegative powers of the n-th prime.

1, 4, 31, 400, 16105, 402234, 25646167, 943531280, 81870575521, 15025258332150, 846949229880161, 182859777940000980, 23127577557875340733, 1759175174860440565844, 262246703278703657363377, 74543635579202247026882160, 21930887362370823132822661921, 2279217547342466764922495586798

Offset: 1

Author

Omar E. Pol, Sep 11 2018

Keywords

• nonn

Examples

			For n = 4 the 4th prime is 7 and the sum of the first four nonnegative powers of 7 is 7^0 + 7^1 + 7^2 + 7^3 = 1 + 7 + 49 + 343 = 400, so a(4) = 400.
		

Crossrefs

Main diagonal of A319076.

Cf. A000040, A000203, A006093, A062457, A069459, A093360, A319075.

Cf. A000079, A000244, A000351, A000420, A001020, A001022, A001026, A001029, A009967, A009973, A009975, A009981, A009985, A009987, A009991.

Cf. A126646, A003462, A003463, A023000, A016123, A091030, A091045, A218722, A218726, A218732, A218734, A218740, A218744, A218746, A218750.

Programs

PARI

a(n) = sum(k=0, n-1, prime(n)^k); \\ Michel Marcus, Sep 13 2018

Formula

a(n) = Sum_{k=0..n-1} A000040(n)^k.

a(n) = Sum_{k=0..n-1} A319075(k,n).

a(n) = (A000040(n)^n - 1)/(A000040(n) - 1).

a(n) = (A062457(n) - 1)/A006093(n).

a(n) = A069459(n)/A006093(n).

a(n) = A000203(A000040(n)^(n-1)).

a(n) = A000203(A093360(n)).