A177441 Partial sums of A014597.

1, 4, 9, 20, 32, 59, 88, 159, 231, 444, 659, 1262, 1897, 3814, 1187707

Offset: 1

Author

Jonathan Vos Post, May 08 2010

Keywords

• hard
• nonn

Comments

Partial sums of numbers n such that n^2 is a sum of distinct factorials. The subsequence of primes in this partial sum begins: 59, 659, 1187707. If there is a larger value (the sequence might be finite), a(n)^2 must be greater than 48! (about 1.24139 * 10^61).

Examples

			a(15) = 1 + 3 + 5 + 11 + 12 + 27 + 29 + 71 + 72 + 213 + 215 + 603 + 635 + 1917 + 1183893 is prime.
		

Crossrefs

Cf. A000142, A014597, A025494, A051761, A059589.

Formula

a(n) = SUM[i=1..n] A014597(i) = SUM[i=1..n] {i such that i^2 is a sum of distinct factorials} = SUM[i=1..n] {i such that i^2 is a sum of distinct A000142(j)}.