A074309 Sum of next n terms of the form i^i.

4, 283, 50037, 17650540, 10405067904, 9211817140115, 11424093748466841, 18896062057822100616, 40192544399240309019728, 106876212200059543898143707, 347377340594805599176614321101

Offset: 1

Author

Zak Seidov, Sep 22 2002

Keywords

• nonn

Comments

Sum of next n terms of the form i^n is A074209. Sum of first n terms of the form i^n is A031971. Sum of first n terms of the form i^i is A001923.

Examples

			a(2) = 283 = 3^3 + 4^4, a(3) = 50037 = 4^4 + 5^5 + 6^6, a(4) = 17650540 = 5^5 + 6^6 + 7^7 + 8^8, a(5) = 10405067904 = 6^6 + 7^7 + 8^8 + 9^9 + 10^10.
		

Links

• Seiichi Manyama, Table of n, a(n) for n = 1..193

Crossrefs

Cf. A001923, A031971, A074209.

Programs

Mathematica

Table[Sum[i^i, {i, n+1, 2n}], {n, 20}]

PARI

a(n) = sum(k=n+1, 2*n, k^k); \\ Seiichi Manyama, Dec 05 2021

Formula

a(n) = Sum_{i=n+1..2n} i^i.

a(n) ~ (2*n)^(2*n). - Vaclav Kotesovec, Dec 06 2021