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 A353355 #24 Apr 24 2022 17:20:56
%S A353355 1,4,6,8,9,12,14,15,18,20,25,26,27,28,32,33,35,36,38,44,45,48,49,50,
%T A353355 51,52,58,60,63,64,65,68,69,72,74,75,76,77,84,86,90,92,93,95,96,98,99,
%U A353355 100,106,108,110,112,116,117,119,120,121,122,123,124,125,126,132,140,141,142,143,144,145,147,148,150,153,156
%N A353355 Numbers k for which A353328(k) is equal to A353329(k).
%C A353355 Numbers k such that A353354(k) [= Sum_{d|k} A332823(d)] is zero.
%C A353355 If k is present, then A003961(k), A348717(k) and (for all m >= 1) k*m^3 are present also.
%C A353355 Includes all numbers whose number of divisors is a multiple of 3 (A059269). Each number in A059269 has its divisors equally distributed between the classes defined by A332823; and they are exactly the numbers, m, for which A353354(m) = A353446(m) = 0.
%H A353355 <a href="/index/Pri#prime_indices">Index entries for sequences computed from indices in prime factorization</a>
%o A353355 (PARI)
%o A353355 A332823(n) = { my(f = factor(n),u=(sum(k=1, #f~, f[k, 2]*2^primepi(f[k, 1]))/2)%3); if(2==u,-1,u); };
%o A353355 A353354(n) = sumdiv(n,d,A332823(d));
%o A353355 isA353355(n) = (0==A353354(n));
%Y A353355 Positions of 0's in A353354.
%Y A353355 Union of A059269 and A332820.
%Y A353355 A353356, A353357 and this sequence partition the natural numbers to three disjoint sets, based on the values obtained by A353354.
%Y A353355 Cf. A003961, A048675, A332823, A348717, A353328, A353329, A353352, A353354, A353380 (characteristic function), A353382, A353414, A353446.
%Y A353355 Cf. A000578, A001248, A059269 (subsequences).
%K A353355 nonn
%O A353355 1,2
%A A353355 _Antti Karttunen_ and _Peter Munn_, Apr 15 2022