A174226 Partial sums of A034897.

6, 27, 55, 356, 681, 1177, 1874, 3207, 5116, 7157, 9290, 13191, 21319, 32012, 48525, 68046, 92647, 119624, 170925, 267286, 397439, 557280, 720481, 897142, 1111415, 1361736, 1637569, 1933910, 2240091, 2629684, 3116561, 3612090, 4154503

Offset: 1

Author

Jonathan Vos Post, Mar 12 2010

Keywords

• nonn

Comments

Partial sums of hyperperfect numbers. The subsequence of prime values in this partial sum begins: 21319, 92647, 720481.

Examples

			a(x) = 6 + 21 + 28 + 301 + 325 + 496 + 697 + 1333 + 1909 + 2041 + 2133 + 3901 + 8128 + 10693 + 16513 + 19521 + 24601 = 92647 is prime.
		

Crossrefs

Cf. A034897, A034898, A007592, A019279.

Formula

a(n) = SUM[i=1..n] A034897(i) = SUM[i=1..n] {m such that k*sigma(m) = (k+1)*m + k - 1 for some positive integer k, and sigma being the divisor function A000005; noting that k=1 gives perfect numbers}.