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.

A100696 Weird numbers m such that the sum of their divisors below A033880(m) is greater than A033880(m) = abundance of m.

Original entry on oeis.org

9272, 222952, 243892, 338572, 343876, 351956, 407132, 410476, 465652, 1188256, 1229152, 1901728, 2081824, 2189024, 3963968, 4199030, 4486208, 4559552, 5440192, 5568448, 5681270, 5763310, 5780810, 5804330, 5823790, 5921090, 6365870, 6460864, 6543110, 6911512
Offset: 1

Views

Author

N. J. A. Sloane, based on email from Alexey Aleksandrov (aleksandrov1988(AT)gmail.com), Mar 28 2006

Keywords

Comments

This sequence was posed as a puzzle by Prof. E. A. Roganov from Moscow State Industrial University at one of his seminars. It remained unsolved for several years. The solution (cf. current definition) was eventually revealed by the author (communicated by Max Alekseyev on Apr 19 2012).
It may be easily noticed that for an abundant number m, if the sum of its divisors below A033880(m) is smaller than A033880(m), then m is necessarily weird. So A100696 lists those weird numbers that cannot be detected this way. - Max Alekseyev, Apr 19 2012

Links

Crossrefs

Cf. A033880.
Intersection of A006037 and A182225.

Programs

  • PARI
    is_A100696(n,d=divisors(n)[^-1],a=vecsum(d)-n,s=a)={for(i=1,#d,d[i]0||break); !is_A005835(n,d,a+n)} \\ M. F. Hasler, Jul 30 2016

Extensions

a(14)-a(30) from Donovan Johnson, Apr 19 2012
Data up to 10^7 double-checked by M. F. Hasler, Jul 30 2016

A182226 Abundant numbers m (in A005101) whose sum of divisors less than their abundance A033880(m) does not exceed A033880(m).

Original entry on oeis.org

18, 20, 70, 78, 88, 102, 104, 114, 138, 174, 186, 196, 222, 246, 258, 282, 318, 354, 366, 368, 402, 426, 438, 464, 474, 498, 534, 582, 606, 618, 642, 650, 654, 678, 762, 786, 822, 834, 836, 894, 906, 942, 978, 1002, 1014, 1038, 1074, 1086, 1146, 1158, 1182, 1194, 1266, 1338, 1362, 1374, 1398
Offset: 1

Views

Author

M. F. Hasler, Apr 19 2012

Keywords

Comments

Complement of A182225 in A005101.

Links

Programs

  • Mathematica
    aQ[n_] := (ab = DivisorSigma[1, n] - 2 n) > 0 && DivisorSum[n, # &, # < ab &] <= ab; Select[Range[1400], aQ] (* Amiram Eldar, Sep 08 2019 *)
  • PARI
    for(n=1,1999,sigma(n)>2*n||next;is_A182225(n)||print1(n","))

A182227 Sum of divisors of the abundant number m = A005101(n) which are smaller than its abundance A033880(m).

Original entry on oeis.org

6, 3, 1, 24, 27, 55, 20, 19, 76, 21, 14, 108, 23, 3, 123, 12, 66, 140, 3, 144, 156, 22, 12, 1, 172, 52, 12, 240, 123, 204, 12, 126, 259, 147, 236, 138, 66, 312, 12, 42, 546, 12, 316, 7, 171, 165, 198, 44, 366, 384, 174, 12, 112, 218, 117, 744, 12, 476, 12, 198
Offset: 1

Views

Author

M. F. Hasler, Apr 19 2012

Keywords

Comments

Motivated by A100696. See also A182225 and A182226.

Links

Crossrefs

Cf. A005101, A033880, A100696, A182225, A182226.

Programs

  • Mathematica
    f[n_] := If[(ab = DivisorSigma[1, n] - 2*n) > 0 ,DivisorSum[n, # &, # < ab &],Nothing]; Array[f, 300] (* Amiram Eldar, Apr 06 2024 *)
  • PARI
    f(n)=my(A=sigma(n)-2*n,s);fordiv(n,d,(d2*n & print1(f(n)","))
Showing 1-3 of 3 results.

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

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