cp's OEIS Frontend

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.

Showing 1-3 of 3 results.

A324652 Numbers k such that A318468(k) (bitwise-AND of 2*k and sigma(k)) is equal to 2*k.

Original entry on oeis.org

6, 12, 18, 20, 24, 28, 36, 40, 48, 56, 80, 88, 96, 100, 104, 112, 160, 176, 192, 196, 200, 204, 208, 220, 224, 260, 264, 272, 304, 320, 336, 352, 368, 384, 392, 416, 448, 464, 496, 544, 550, 580, 608, 640, 648, 650, 672, 704, 736, 768, 784, 832, 896, 928, 992, 1032, 1040, 1044, 1056, 1060, 1068, 1088, 1104, 1120, 1184, 1216
Offset: 1

Views

Author

Antti Karttunen, Mar 14 2019

Keywords

Comments

Positions of zeros in A324658, fixed points of A324659.
Intersection with A324649 gives A324643.
Intersection with A324726 gives A000396.
In the range 1..2^32 there are only 22 odd terms. See A324647.

Links

Crossrefs

Cf. A000203, A191218, A318468, A324647, A324649, A324658, A324659, A324722, A324726.
Some subsequences: A000396, A324643, A324647 (the odd terms).

Programs

  • Mathematica
    Select[Range[2000], 2*# == BitAnd[2*#, DivisorSigma[1, #]] &] (* Paolo Xausa, Mar 11 2024 *)
  • PARI
    for(n=1,oo,if((n+n)==bitand(2*n,sigma(n)), print1(n, ", ")))

A324649 Numbers k such that A318458(k) (bitwise-AND of k and sigma(k)-k) is equal to k.

Original entry on oeis.org

6, 20, 28, 36, 66, 72, 88, 100, 104, 114, 132, 150, 240, 258, 264, 272, 280, 304, 354, 368, 392, 402, 464, 496, 498, 516, 550, 552, 642, 644, 680, 708, 748, 770, 774, 784, 786, 834, 836, 840, 860, 978, 1026, 1032, 1040, 1044, 1056, 1062, 1064, 1068, 1074, 1092, 1104, 1120, 1184, 1232, 1266, 1312, 1362, 1376, 1410, 1504
Offset: 1

Views

Author

Antti Karttunen, Mar 14 2019

Keywords

Comments

Positions of zeros in A324648. Fixed points of A318458, also positions of the records in the latter.
Intersection with A324652 gives A324643.
The odd terms are: 7425, 76545, 92565, ... (A324897).

Links

Crossrefs

Cf. A318458, A324648, A324652.
Cf. A000396, A324643, A324897, A324898 (subsequences).

Programs

  • Mathematica
    Select[Range@ 1600, BitAnd[#, DivisorSigma[1, #] - #] == # &] (* Michael De Vlieger, Apr 21 2019, after Vincenzo Librandi at A318458 *)
  • PARI
    for(n=1,oo,if(bitand(n,sigma(n)-n)==n, print1(n, ", ")));

A324639 Numbers k such that bitand(2k,sigma(k)) = 2*bitand(k,sigma(k)-k), where bitand is bitwise-AND, A004198.

Original entry on oeis.org

1, 2, 4, 5, 6, 8, 9, 10, 16, 17, 20, 26, 28, 32, 36, 37, 38, 41, 44, 50, 64, 73, 74, 88, 98, 100, 104, 128, 130, 134, 136, 137, 149, 152, 153, 164, 172, 184, 256, 257, 261, 262, 264, 272, 277, 284, 293, 294, 304, 328, 337, 368, 392, 405, 410, 424, 442, 464, 496, 512, 520, 521, 522, 528, 529, 538, 548, 549, 550, 556, 560, 577
Offset: 1

Views

Author

Antti Karttunen, Mar 14 2019

Keywords

Comments

Numbers k for which 2*A318458(k) = A318468(k).

Links

Crossrefs

Cf. A004198, A318458, A318468.
Subsequences: A324643, A324718 (odd terms).

Programs

  • Mathematica
    Select[Range[1000], Block[{s = DivisorSigma[1, #]}, BitAnd[2*#, s] == 2* BitAnd[#, s-#]] &] (* Paolo Xausa, Mar 11 2024 *)
  • PARI
    for(n=1,oo,if( (2*(bitand(n, sigma(n)-n))==bitand(n+n, sigma(n))),print1(n,", ")));
Showing 1-3 of 3 results.

Started in 1964 by Neil J. A. Sloane | Maintained by The OEIS Foundation Inc.

Content is available under The OEIS End-User License Agreement.