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 1-5 of 5 results.

A380846 Numbers k such that A380845(k) = 2*k.

Original entry on oeis.org

18, 42, 90, 186, 196, 306, 378, 420, 534, 618, 654, 690, 762, 834, 868, 906, 1062, 1110, 1194, 1242, 1326, 1362, 1422, 1458, 1530, 1698, 1764, 1818, 1866, 2118, 2214, 2262, 2324, 2346, 2490, 2598, 2670, 2706, 2730, 2778, 2838, 2862, 2884, 2922, 2958, 2994, 3066, 3138
Offset: 1

Views

Author

Amiram Eldar, Feb 05 2025

Keywords

Comments

Analogous to perfect numbers (A000396) with A380845 instead of A000203.
All the terms are abundant numbers (A005101), since A380845(k) <= A000203(k) with equality only when k is a power of 2, and powers of 2 are deficient numbers (A005100).
Are there odd terms in this sequence? There are none below 10^11.

Examples

			18 is a term since A380845(18) = 36 = 2 * 18.

Links

Crossrefs

Cf. A000203, A000396, A005100, A380845, A380847, A380848.
Subsequence of A005101.

Programs

  • Mathematica
    q[k_] := Module[{h = DigitCount[k, 2, 1]}, DivisorSum[k, # &, DigitCount[#, 2, 1] == h &] == 2*k]; Select[Range[3200], q]
  • PARI
    isok(k) = {my(h = hammingweight(k)); sumdiv(k, d, d*(hammingweight(d) == h)) == 2*k;}

A380929 Numbers k such that A380845(k) > 2*k.

Original entry on oeis.org

36, 72, 84, 140, 144, 168, 180, 264, 270, 280, 288, 300, 336, 360, 372, 392, 450, 520, 528, 532, 540, 558, 560, 576, 594, 600, 612, 620, 672, 720, 744, 756, 780, 784, 840, 900, 930, 1036, 1040, 1050, 1056, 1064, 1068, 1080, 1092, 1116, 1120, 1134, 1152, 1170, 1180, 1188, 1200
Offset: 1

Views

Author

Amiram Eldar, Feb 08 2025

Keywords

Comments

Analogous to abundant numbers (A005101) with A380845 instead of A000203.

Examples

			36 is a term since A380845(36) = 84 > 2 * 36 = 72.

Links

Crossrefs

Cf. A000203, A380845, A380846.
Subsequence of A005101.
Subsequences: A380847, A380848, A380930, A380931.
Similar sequences: A034683, A064597, A087248, A129575, A129656, A292982, A348274, A348604, A379029.

Programs

  • Mathematica
    q[k_] := Module[{h = DigitCount[k, 2, 1]}, DivisorSum[k, # &, DigitCount[#, 2, 1] == h &] > 2*k]; Select[Range[1200], q]
  • PARI
    isok(k) = {my(h = hammingweight(k)); sumdiv(k, d, d*(hammingweight(d) == h)) > 2*k;}

A380848 Numbers k such that A380845(k) = 4*k.

Original entry on oeis.org

123832800, 247695840, 268337160, 495421920, 536707080, 990874080, 1073446920, 1981778400, 2146926600, 3963587040, 4293885960, 7927204320, 8587804680, 15854438880, 17175642120, 31708908000, 34351317000, 63417846240, 68702666760, 124884879840, 126713795040, 126835722720
Offset: 1

Views

Author

Amiram Eldar, Feb 05 2025

Keywords

Comments

Analogous to 4-perfect numbers (A027687) with A380845 instead of A000203.
All the terms are 4-abundant numbers (A068404), because A380845(k) <= A000203(k) with equality only when k is a power of 2, and powers of 2 are deficient numbers (A005100).
Are there numbers k such that A380845(k) = m*k for integers m >= 5? There are none below 1.6*10^11.

Crossrefs

Cf. A000203, A005100, A027687, A380845, A380846, A380847.
Subsequence of A068404.

Programs

  • Mathematica
    q[k_] := Module[{h = DigitCount[k, 2, 1]}, DivisorSum[k, # &, DigitCount[#, 2, 1] == h &] == 4*k]; Select[Range[3*10^8], q]
  • PARI
    isok(k) = {my(h = hammingweight(k)); sumdiv(k, d, d*(hammingweight(d) == h)) == 4*k;}

Extensions

a(19)-a(22) from Jinyuan Wang, Feb 12 2025

A380931 Numbers k such that A380845(k) > 4*k.

Original entry on oeis.org

5155920, 7733880, 10311840, 15467760, 20623680, 30935520, 41247360, 46403280, 61871040, 61901280, 75546240, 82494720, 87693480, 92806560, 103168800, 103194000, 113513400, 123742080, 123802560, 134152200, 140540400, 151092480, 151351200, 162162000, 164989440, 175386960
Offset: 1

Views

Author

Amiram Eldar, Feb 08 2025

Keywords

Comments

Analogous to 4-abundant numbers (A068404) with A380845 instead of A000203.

Examples

			5155920 is a term since A380845(5155920) = 21067042 > 4 * 5155920 = 20623680.

Links

Crossrefs

Cf. A000203, A380845, A380846, A380847, A380848.
Subsequence of A068404, A380929 and A380931.
Similar sequences: A307114, A340110.

Programs

  • Mathematica
    q[k_] := Module[{h = DigitCount[k, 2, 1]}, DivisorSum[k, # &, DigitCount[#, 2, 1] == h &] > 4*k]; Select[Range[10^8], q]
  • PARI
    isok(k) = {my(h = hammingweight(k)); sumdiv(k, d, d*(hammingweight(d) == h)) > 4*k;}

A380930 Numbers k such that A380845(k) > 3*k.

Original entry on oeis.org

1080, 2160, 3600, 4320, 7200, 7440, 8640, 11340, 13608, 14400, 14880, 15120, 17280, 18600, 22680, 22860, 27216, 28800, 29760, 30240, 30480, 31752, 33264, 34020, 34560, 37200, 41664, 45360, 45720, 45900, 51408, 53340, 54432, 57600, 59520, 60480, 60960, 61200, 63504
Offset: 1

Views

Author

Amiram Eldar, Feb 08 2025

Keywords

Comments

Analogous to 3-abundant numbers (A068403) with A380845 instead of A000203.

Links

Crossrefs

Cf. A000203, A380845, A380846, A380847.
Subsequence of A068403 and A380929.
Subsequences: A380848, A380931.
Similar sequences: A285615, A293187, A300664, A328135, A340109.

Programs

  • Mathematica
    q[k_] := Module[{h = DigitCount[k, 2, 1]}, DivisorSum[k, # &, DigitCount[#, 2, 1] == h &] > 3*k]; Select[Range[64000], q]
  • PARI
    isok(k) = {my(h = hammingweight(k)); sumdiv(k, d, d*(hammingweight(d) == h)) > 3*k;}

Formula

1080 is a term since A380845(1080) = 3330 > 3 * 1080 = 3240.
Showing 1-5 of 5 results.

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