A382664 Partial sums of the exponentially odd numbers (A268335).

1, 3, 6, 11, 17, 24, 32, 42, 53, 66, 80, 95, 112, 131, 152, 174, 197, 221, 247, 274, 303, 333, 364, 396, 429, 463, 498, 535, 573, 612, 652, 693, 735, 778, 824, 871, 922, 975, 1029, 1084, 1140, 1197, 1255, 1314, 1375, 1437, 1502, 1568, 1635, 1704, 1774, 1845, 1918

Offset: 1

Author

Amiram Eldar, Apr 02 2025

Keywords

• nonn
• easy

Links

• Amiram Eldar, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A065489, A268335.

Similar sequences: A173143, A174172, A358038, A362971.

Programs

Mathematica

Accumulate[Select[Range[100], AllTrue[FactorInteger[#][[;; , 2]], OddQ] &]]

PARI

isexpodd(n) = {my(f = factor(n)); for(i=1, #f~, if(!(f[i, 2] % 2), return (0))); 1;}
list(lim) = {my(s = 0); for(k = 1, lim, if(isexpodd(k), s += k; print1(s, ", "))); }

Formula

a(n) = Sum_{k=1..n} A268335(k).

a(n) ~ c * n^2 / 2, where c = Product_{p prime} (1 + 1/(p^2+p-1)) = 1.419562... (A065489).