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A332465 Numbers n for which A269174(sigma(n)) is equal to 2*A269174(n). 3

%I

%S 6,28,348,496,732,886,2924,3573,4972,5448,7544,8128,23388,54842,66928,

%T 89200,92296,109786,118064,121552,349512,356488,367472,550432,634784,

%U 839984,842452,1234048,1561408,1797496,2154584,2364832,2788808,2927992,3451456,3585328,5952364,5991852,6687136,8238752,10594336,11210712,11261020

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

%C Numbers n such that A332464(n) is equal to A269174(2*n).

%C 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 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 Antti Karttunen, <a href="/A332465/b332465.txt">Table of n, a(n) for n = 1..113; all terms <= 2^32</a>

%H <a href="/index/O#opnseqs">Index entries for sequences where any odd perfect numbers must occur</a>

%H <a href="/index/Si#SIGMAN">Index entries for sequences related to sigma(n)</a>

%e k factorization sigma(k) A269174(sigma(k)) = A269174(2*k)

%e 348 = 2^2 * 3 * 29 840 2008,

%e 3573 = 3^2 * 397 5174 15486,

%e 29255157 = 3^2 * 3250573 42257462 126737534,

%e 936109557 = 3^2 * 104012173 1352158262 4055424126.

%t b[n_] := BitAnd[BitOr[n, 2n], BitOr[BitXor[n, 2n], BitXor[n, 4n]]];

%t okQ[n_] := b[DivisorSigma[1, n]] == 2 b[n];

%t Reap[For[n = 1, n <= 12*10^6, n++, If[okQ[n], Print[n]; Sow[n]]]][[2, 1]] (* _Jean-Fran├žois Alcover_, Feb 23 2020 *)

%o (PARI)

%o A269174(n) = bitand(bitor(n,n<<1),bitor(bitxor(n,n<<1),bitxor(n,n<<2)));

%o isA332465(n) = (A269174(sigma(n))==2*A269174(n));

%Y Cf. A000203, A269174, A332464.

%Y Cf. A000396 (a subsequence).

%Y Cf. also A191218, A228058, A332227, A332445, A332446.

%K nonn

%O 1,1

%A _Antti Karttunen_, Feb 16 2020

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Last modified July 9 11:58 EDT 2020. Contains 335543 sequences. (Running on oeis4.)