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

Author

Jonathan Vos Post, Aug 26 2005

Keywords

• easy
• nonn

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.

Crossrefs

Cf. A000026.

Programs

Mathematica

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

Formula

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

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