A109443 Cumulative sum of largest prime power <= n.

1, 3, 6, 10, 15, 20, 27, 35, 44, 53, 64, 75, 88, 101, 114, 130, 147, 164, 183, 202, 221, 240, 263, 286, 311, 336, 363, 390, 419, 448, 479, 511, 543, 575, 607, 639, 676, 713, 750, 787, 828, 869, 912, 955, 998

Offset

1,2

Comments

Integers in this sequence which are themselves primes include a(2) = 3, a(10) = 53, a(14) = 101, a(23) = 263, a(25) = 311, a(29) = 419, a(31) = 479, a(35) = 607, a(40) = 787. Integers in this sequence which are themselves powers greater than 1 of primes include a(7) = 27, a(11) = 64. Integers in this sequence which are perfect powers greater than 1 of composites include a(37) = 676.

Links

Table of n, a(n) for n=1..45.

Formula

a(n) = Sum_{i=1..n} A031218(i).

Crossrefs

Cf. A031218.

Sequence in context: A033438 A037452 A047800 * A138777 A096895 A034175

Adjacent sequences: A109440 A109441 A109442 * A109444 A109445 A109446

Keyword

easy,nonn

Author

Jonathan Vos Post, Aug 26 2005

Status

approved