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A332465 Numbers n for which A269174(sigma(n)) is equal to 2*A269174(n).

%I A332465 #25 Feb 23 2020 07:42:26
%S A332465 6,28,348,496,732,886,2924,3573,4972,5448,7544,8128,23388,54842,66928,
%T A332465 89200,92296,109786,118064,121552,349512,356488,367472,550432,634784,
%U A332465 839984,842452,1234048,1561408,1797496,2154584,2364832,2788808,2927992,3451456,3585328,5952364,5991852,6687136,8238752,10594336,11210712,11261020
%N A332465 Numbers n for which A269174(sigma(n)) is equal to 2*A269174(n).
%C A332465 Numbers n such that A332464(n) is equal to A269174(2*n).
%C A332465 There are only three odd terms <= 2^32 among the first 113 terms of this sequence: 3573, 29255157, 936109557. Because A269174 preserves the 2-adic valuation of its argument, all such odd terms are of the form 4m+1, and must be present in A191218. Incidentally, these three terms are also present in A228058, but not in A332227.
%C A332465 See from the graph how unevenly the terms appear. Compare also the scatter plots of A269174 and A332464, also of a similar sequence A332445.
%H A332465 Antti Karttunen, <a href="/A332465/b332465.txt">Table of n, a(n) for n = 1..113; all terms <= 2^32</a>
%H A332465 <a href="/index/O#opnseqs">Index entries for sequences where any odd perfect numbers must occur</a>
%H A332465 <a href="/index/Si#SIGMAN">Index entries for sequences related to sigma(n)</a>
%e A332465           k   factorization        sigma(k)     A269174(sigma(k)) = A269174(2*k)
%e A332465         348 = 2^2 * 3 * 29         840          2008,
%e A332465        3573 = 3^2 * 397            5174         15486,
%e A332465    29255157 = 3^2 * 3250573        42257462     126737534,
%e A332465   936109557 = 3^2 * 104012173      1352158262   4055424126.
%t A332465 b[n_] := BitAnd[BitOr[n, 2n], BitOr[BitXor[n, 2n], BitXor[n, 4n]]];
%t A332465 okQ[n_] := b[DivisorSigma[1, n]] == 2 b[n];
%t A332465 Reap[For[n = 1, n <= 12*10^6, n++, If[okQ[n], Print[n]; Sow[n]]]][[2, 1]] (* _Jean-François Alcover_, Feb 23 2020 *)
%o A332465 (PARI)
%o A332465 A269174(n) = bitand(bitor(n,n<<1),bitor(bitxor(n,n<<1),bitxor(n,n<<2)));
%o A332465 isA332465(n) = (A269174(sigma(n))==2*A269174(n));
%Y A332465 Cf. A000203, A269174, A332464.
%Y A332465 Cf. A000396 (a subsequence).
%Y A332465 Cf. also A191218, A228058, A332227, A332445, A332446.
%K A332465 nonn
%O A332465 1,1
%A A332465 _Antti Karttunen_, Feb 16 2020