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 1-4 of 4 results.

A383932 Integers k such that there exists an integer 0

Original entry on oeis.org

84, 102, 160, 186, 276, 284, 330, 582, 624, 762, 868, 1164, 1210, 1372, 1404, 1446, 1488, 1540, 1988, 2156, 2640, 2716, 2898, 2924, 3556, 3708, 3882, 4074, 4228, 4536, 5382, 5564, 5610, 5802, 6018, 6282, 6368, 6392, 6486, 6612, 6748, 7140, 7452, 7494, 7960, 8358, 8432, 9222, 9834
Offset: 1

Views

Author

S. I. Dimitrov, May 15 2025

Keywords

Comments

The numbers m and k form a GM-amicable pair. See Dimitrov link.

Examples

			For k=2 we have (28, 84), (42, 102), (60, 276), (92, 160).

Links

Crossrefs

Cf. A063990, A259180, A383239, A383483, A383484.

Programs

  • PARI
    isok(k) = for (m=1, k-1, if (sigma(m)*sigma(k) == (m+k)^2, return(m))); \\ Michel Marcus, May 15 2025

Extensions

More terms from Michel Marcus, May 15 2025

A383964 Integers k such that there exists an integer 0

Original entry on oeis.org

168, 1320, 3792, 4968, 7176, 8184, 14364, 15240, 20076, 29904, 30672, 41952, 48312, 48768, 54264, 56856, 57960, 60144, 64296, 72996, 73344, 83328, 90552, 91512, 99828, 106020, 110952, 113280, 114156, 119016, 128592, 149292, 150024, 151272, 157608, 168588, 175584, 183240
Offset: 1

Views

Author

S. I. Dimitrov, May 16 2025

Keywords

Comments

The numbers m and k form a HM(2,1)-amicable pair (HM = harmonic mean). See Dimitrov link.

Examples

			(120, 168) is such a pair because (1/sigma(120)^2 + 1/sigma(168)^2)*(120+168)^2 = 1.

Links

Crossrefs

Cf. A063990, A259180, A383239, A383483, A383484.

Programs

  • PARI
    isok(k) = for(m=1, k-1, if((1/sigma(m)^2 + 1/sigma(k)^2)*(m+k)^2 == 1, return(m))); \\ Michel Marcus, May 16 2025

Extensions

a(7) and a(9)-a(25) from Michel Marcus, May 16 2025
More terms from David A. Corneth, Jun 21 2025

A383714 Integers k such that there exists an integer 0

Original entry on oeis.org

21, 231, 284, 1210, 2499, 2924, 5564, 6368, 10856, 14595, 18416, 66992, 71145, 76084, 87633, 88730
Offset: 1

Views

Author

S. I. Dimitrov, May 14 2025

Keywords

Comments

The numbers m and k form a WPM(2)-amicable pair (WPM = weighted power mean). See Dimitrov link.

Examples

			(7, 21) is such a pair because 7*sigma(7)^2 + 21*sigma(21)^2 = 7*8^2 + 21*32^2 = (7+21)^3.

Links

Crossrefs

Cf. A002046 (a subsequence), A063990, A259180, A383239, A383483, A383484.

Programs

  • PARI
    isok(k)= for (m=1, k-1, if (m*sigma(m)^2 + k*sigma(k)^2 == (m+k)^3, return(m))); \\ Michel Marcus, May 15 2025

Extensions

a(3)-a(16) from Michel Marcus, May 15 2025

A384411 Pairs (k, m) such that k = sigma(m) - m and m = sigma(2*k) - 2*k.

Original entry on oeis.org

26, 46, 296, 586
Offset: 1

Views

Author

S. I. Dimitrov, Jun 01 2025

Keywords

Comments

Fixed points of x->A346878(A001065(x)).
Next term > 15*10^7.

Examples

			(26, 46) is such a pair because 26 = sigma(46) - 46 and 46 = sigma(52) - 52.
(296, 586) is another pair.

Links

Crossrefs

Cf. A000203, A001065, A063990, A259180, A346878, A383483.

Programs

  • PARI
    for(k=1,10^9, m = sigma(2*k) - 2*k;if(k == sigma(m) - m, print1(k, ", ", m, ", "))); \\ Joerg Arndt, Jun 01 2025
Showing 1-4 of 4 results.

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

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