A109444 Cumulative sum of mosaic numbers (A000026).

1, 3, 6, 10, 15, 21, 28, 34, 40, 50, 61, 73, 86, 100, 115, 123, 140, 152, 171, 191, 212, 234, 257, 275, 285, 311, 320, 348, 377, 407, 438, 448, 481, 515, 550, 574, 611, 649, 688, 718, 759, 801, 844, 888, 918, 964, 1011, 1035, 1049, 1069, 1120, 1172, 1225

Offset

1,2

Comments

Integers in this sequence which are themselves primes include a(2) = 3, a(11) = 61, a(12) = 73, a(20) = 191, a(23) = 257, a(26) = 311, a(62) = 1697, a(67) = 1949, a(68) = 2017. Integers in this sequence which are perfect powers greater than 1 of composites include a(14) = 100, a(53) = 1225.

Links

Table of n, a(n) for n=1..53.

Formula

A000026(Product (p_j^k_j)) = Product (p_j * k_j).

a(n) = Sum_{i=1..n} A000026(i).

Mathematica

Accumulate[Array[Times@@Flatten[FactorInteger[#]]&, 60]] (* Harvey P. Dale, Sep 16 2018 *)

Crossrefs

Cf. A000026.

Sequence in context: A231680 A124158 A161208 * A124157 A033440 A067525

Adjacent sequences: A109441 A109442 A109443 * A109445 A109446 A109447

Keyword

easy,nonn

Author

Jonathan Vos Post, Aug 26 2005

Status

approved