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

1,2

Links

Table of n, a(n) for n=1..18.

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)).

Example

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.

Prog

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

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.

Sequence in context: A174324 A211194 A237581 * A195195 A141827 A262529

Adjacent sequences: A319071 A319072 A319073 * A319075 A319076 A319077

Keyword

nonn

Author

Omar E. Pol, Sep 11 2018

Status

approved