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 A357015 #8 Sep 09 2022 06:30:43 %S A357015 81,405,567,625,891,1053,1377,1539,1863,1875,2349,2401,2511,2835,2997, %T A357015 3321,3483,3807,4293,4375,4455,4779,4941,5265,5427,5751,5913,6237, %U A357015 6399,6723,6875,6885,7203,7209,7371,7695,7857,8125,8181,8343,8667,8829,9153,9315,9639 %N A357015 Nonsquarefree numbers whose sum of exponential divisors (A051377) is odd. %C A357015 The squarefree numbers are excluded from this sequence since the sum of the exponential divisors of any squarefree number k is A005117(k) = k, so the sum of the exponential divisors of any odd squarefree number (A056911) is odd. %C A357015 Equivalently, odd nonsquarefree numbers whose exponents in their prime factorization are squares. %C A357015 The asymptotic density of this sequence is A357017 - 4/Pi^2 = 0.0045127121... . %H A357015 Amiram Eldar, <a href="/A357015/b357015.txt">Table of n, a(n) for n = 1..10000</a> %e A357015 81 = 3^4 is a term since it is not squarefree and A051377(81) = 93 is odd. %t A357015 f[p_, e_] := DivisorSum[e, p^# &]; esigma[1] = 1; esigma[n_] := Times @@ f @@@ FactorInteger[n]; Select[Range[10^4], ! SquareFreeQ[#] && OddQ[esigma[#]] &] %Y A357015 Intersection of A013929 and A357014. %Y A357015 Cf. A005117, A051377, A056911, A185199. %K A357015 nonn %O A357015 1,1 %A A357015 _Amiram Eldar_, Sep 09 2022