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%I #18 May 03 2022 14:37:49
%S 81,162,243,324,405,486,567,625,648,810,891,972,1053,1134,1215,1250,
%T 1296,1377,1539,1620,1701,1782,1863,1875,1944,2106,2268,2349,2401,
%U 2430,2500,2511,2592,2673,2754,2835,2997,3078,3125,3159,3240,3321,3402,3483,3564,3726,3750,3807,3888,4131,4212,4293,4375,4455,4536
%N Numbers k such that A353627(k) is less than A353628(k).
%C Numbers in A353511 but not in A122132. Positions where A353627 and A353628 differ from each other. See discussion in A209635.
%C a(8) = 625 is the first term that is not a multiple of 81.
%C If k is present in the sequence, then 2*k and A000265(k) are present also.
%o (PARI)
%o A001001(n) = sumdivmult(n, d, sigma(d)*d); \\ From A001001
%o A353628(n) = (A001001(n)%2);
%o A353627(n) = issquarefree(n>>valuation(n, 2));
%o isA353456(n) = (A353627(n) != A353628(n));
%o (PARI) isA353456(n) = if(issquarefree(n=(n>>valuation(n,2))), 0, my(f=factor(n)); for(k=1,#f~,if((f[k,2]%4)>1, return(0))); (1)); \\ After _Álvar Ibeas_'s Nov 28 2017 comment in A209635
%Y Setwise difference A353511 \ A122132. Subsequence of A038838.
%Y Cf. A000265, A001001, A209635, A353627, A353628.
%K nonn
%O 1,1
%A _Antti Karttunen_, May 03 2022