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

6, 28, 348, 496, 732, 886, 2924, 3573, 4972, 5448, 7544, 8128, 23388, 54842, 66928, 89200, 92296, 109786, 118064, 121552, 349512, 356488, 367472, 550432, 634784, 839984, 842452, 1234048, 1561408, 1797496, 2154584, 2364832, 2788808, 2927992, 3451456, 3585328, 5952364, 5991852, 6687136, 8238752, 10594336, 11210712, 11261020

Offset

1,1

Comments

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

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.

See from the graph how unevenly the terms appear. Compare also the scatter plots of A269174 and A332464, also of a similar sequence A332445.

Links

Antti Karttunen, Table of n, a(n) for n = 1..113; all terms <= 2^32

Index entries for sequences where any odd perfect numbers must occur

Index entries for sequences related to sigma(n)

Example

          k   factorization        sigma(k)     A269174(sigma(k)) = A269174(2*k)
        348 = 2^2 * 3 * 29         840          2008,
       3573 = 3^2 * 397            5174         15486,
   29255157 = 3^2 * 3250573        42257462     126737534,
  936109557 = 3^2 * 104012173      1352158262   4055424126.

Mathematica

b[n_] := BitAnd[BitOr[n, 2n], BitOr[BitXor[n, 2n], BitXor[n, 4n]]];
okQ[n_] := b[DivisorSigma[1, n]] == 2 b[n];
Reap[For[n = 1, n <= 12*10^6, n++, If[okQ[n], Print[n]; Sow[n]]]][[2, 1]] (* Jean-François Alcover, Feb 23 2020 *)

Prog

(PARI)
A269174(n) = bitand(bitor(n, n<<1), bitor(bitxor(n, n<<1), bitxor(n, n<<2)));
isA332465(n) = (A269174(sigma(n))==2*A269174(n));

Crossrefs

Cf. A000203, A269174, A332464.

Cf. A000396 (a subsequence).

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

Sequence in context: A333927 A035527 A220437 * A335290 A173360 A085844

Adjacent sequences: A332462 A332463 A332464 * A332466 A332467 A332468

Keyword

nonn

Author

Antti Karttunen, Feb 16 2020

Status

approved