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

%I A382664 #7 Apr 02 2025 12:44:15
%S A382664 1,3,6,11,17,24,32,42,53,66,80,95,112,131,152,174,197,221,247,274,303,
%T A382664 333,364,396,429,463,498,535,573,612,652,693,735,778,824,871,922,975,
%U A382664 1029,1084,1140,1197,1255,1314,1375,1437,1502,1568,1635,1704,1774,1845,1918
%N A382664 Partial sums of the exponentially odd numbers (A268335).
%H A382664 Amiram Eldar, <a href="/A382664/b382664.txt">Table of n, a(n) for n = 1..10000</a>
%F A382664 a(n) = Sum_{k=1..n} A268335(k).
%F A382664 a(n) ~ c * n^2 / 2, where c = Product_{p prime} (1 + 1/(p^2+p-1)) = 1.419562... (A065489).
%t A382664 Accumulate[Select[Range[100], AllTrue[FactorInteger[#][[;; , 2]], OddQ] &]]
%o A382664 (PARI) isexpodd(n) = {my(f = factor(n)); for(i=1, #f~, if(!(f[i, 2] % 2), return (0))); 1;}
%o A382664 list(lim) = {my(s = 0); for(k = 1, lim, if(isexpodd(k), s += k; print1(s, ", "))); }
%Y A382664 Cf. A065489, A268335.
%Y A382664 Similar sequences: A173143, A174172, A358038, A362971.
%K A382664 nonn,easy
%O A382664 1,2
%A A382664 _Amiram Eldar_, Apr 02 2025