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.
%I A367407 #17 Mar 28 2025 04:35:36
%S A367407 1,2,3,5,6,7,4,10,11,13,14,15,17,19,21,22,23,12,26,9,29,30,31,8,33,34,
%T A367407 35,37,38,39,20,41,42,43,46,47,51,53,18,55,28,57,58,59,61,62,65,66,67,
%U A367407 69,70,71,73,74,77,78,79,82,83,85,86,87,44,89,91,93,94,95,24,97
%N A367407 a(n) = sqrt(A367406(n)).
%C A367407 A permutation of the positive integers.
%H A367407 Amiram Eldar, <a href="/A367407/b367407.txt">Table of n, a(n) for n = 1..10000</a>
%H A367407 <a href="/index/Per#IntegerPermutation">Index entries for sequences that are permutations of the natural numbers</a>
%F A367407 a(n) = sqrt(A064549(A268335(n))).
%F A367407 a(n) = sqrt(A268335(n)*A367417(n)).
%F A367407 a(n) = A268335(n)/A367419(n).
%F A367407 Sum_{k=1..n} a(k) = c * n^2 / 2, where c = (zeta(3)/(zeta(2)*d^2)) * Product_{p prime} (1 - 1/(p^2*(p+1))) = A253905 * A065465 / d^3 = 1.29812028442810841122..., and d = A065463 is the asymptotic density of the exponentially odd numbers (A268335).
%t A367407 s[n_] := Sqrt[n * Times @@ FactorInteger[n][[;;, 1]]]; s /@ Select[Range[100], AllTrue[FactorInteger[#][[;; , 2]], OddQ] &]
%o A367407 (PARI) b(n) = {my(f = factor(n)); prod(i = 1, #f~, if(f[i,2]%2, f[i,1]^(f[i,2]+1), 0));}
%o A367407 lista(kmax) = {my(b1); for(k = 1, kmax, b1 = b(k); if(b1 > 0, print1(sqrtint(b1), ", ")));}
%Y A367407 Cf. A064549, A268335, A367406, A367417, A367419.
%Y A367407 Cf. A065463, A065465, A253905.
%K A367407 nonn,easy
%O A367407 1,2
%A A367407 _Amiram Eldar_, Nov 17 2023