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.

A177052 Ceiling(n/2)-abundant numbers.

Original entry on oeis.org

6, 12, 18, 20, 24, 28, 30, 36, 40, 42, 48, 54, 56, 60, 66, 70, 72, 78, 80, 84, 88, 90, 96, 100, 102, 104, 108, 112, 114, 120, 126, 132, 138, 140, 144, 150, 156, 160, 162, 168, 174, 176, 180, 186, 192, 196, 198, 200, 204, 208, 210, 216, 220, 222, 224, 228
Offset: 1

Views

Author

Vladimir Shevelev, Dec 09 2010

Keywords

Comments

For definition, see A175522.
All positive numbers == 0 (mod 6) are in the sequence (basically A008588). In addition, note that all odd primes are ceiling(n/2)-deficient numbers. The first odd term of the sequence is 315.

Links

Crossrefs

Cf. A177050 (perfect version), A005100, A005101, A175524, A175526, A175811, A175821, A175853.

Programs

  • PARI
    isok(n) = sumdiv(n, d, (d ceil(n/2); \\ Michel Marcus, Feb 08 2016
  • Sage
    is_A177052 = lambda n: sum(ceil(d/2) for d in divisors(n)) > 2*ceil(n/2) # D. S. McNeil, Dec 10 2010

Formula

{n : Sum_{d|n, dA004526(1+d) > A004526(1+n)}. [R. J. Mathar, Dec 11 2010]

A177084 Ceiling(n/3)-perfect numbers.

Original entry on oeis.org

2, 3, 4, 10, 14, 50, 52, 130, 184, 315, 688, 988, 2528, 6490, 35456, 396916, 537088, 538112, 801376, 1297312, 8452096, 8456192, 35221184, 53996590, 134520832, 222469702
Offset: 1

Views

Author

Vladimir Shevelev, Dec 09 2010

Keywords

Comments

For definition, see comment of A175522.

Crossrefs

Cf. A000396, A002264, A175522, A175807, A175853, A177050.

Programs

  • Mathematica
    aQ[n_] := DivisorSum[n, Ceiling[#/3] &, # < n &] == Ceiling[n/3]; Select[Range[10^6], aQ] (* Amiram Eldar, Jul 20 2019 *)
  • Sage
    is_A177084 = lambda n: sum(ceil(d/3) for d in divisors(n)) == 2*ceil(n/3) # D. S. McNeil, Dec 10 2010

Formula

{n: Sum_{d|n, dA002264(2+d) = A002264(2+n)}. - R. J. Mathar, Dec 11 2010

Extensions

a(21)-a(26) from Amiram Eldar, Jul 20 2019

A177511 A053735-perfect numbers.

Original entry on oeis.org

3, 26, 62, 74, 77, 133, 134, 143, 155, 161, 185, 203, 206, 209, 215, 218, 319, 323, 341, 386, 398, 458, 473, 542, 545, 551, 554, 562, 565, 581, 589, 611, 614, 629, 635, 662, 671, 695, 698, 703, 706, 707, 713, 718, 721, 889, 899, 913, 959, 965, 998
Offset: 1

Views

Author

Vladimir Shevelev, Dec 11 2010

Keywords

Comments

For definition, see A175522.

Links

Crossrefs

Cf. A175522, A000396, A175807, A175853, A176234, A177084, A177050.

Programs

  • Maple
    A053735 := proc(n) add(d, d=convert(n,base,3)) ;end proc:
isA177511 := proc(n) local a,d ; a := 0 ; for d in numtheory[divisors](n) minus {n} do a := a+A053735(d) ; end do: a = A053735(n) ;end proc:
for n from 1 to 1000 do if isA177511(n) then printf("%d,",n) ; end if; end do: # R. J. Mathar
  • PARI
    isok(n) = sumdiv(n, d, (dMichel Marcus, Feb 06 2016
  • Sage
    A053735 = lambda n: sum(n.digits(base=3))
is_A177511 = lambda n: sum(A053735(d) for d in divisors(n)) == 2*A053735(n)
# D. S. McNeil, Dec 11 2010

Formula

{n : sum_{d|n, dA053735(d) = A053735(n)}.

Extensions

Extended by D. S. McNeil, Dec 11 2010
Showing 1-3 of 3 results.

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