cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

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

Original entry on oeis.org

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

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Author

Amiram Eldar, Apr 02 2025

Keywords

Crossrefs

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).
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