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.

A317047 Numbers k such that both k and k + 1 are deficient.

Original entry on oeis.org

1, 2, 3, 4, 7, 8, 9, 10, 13, 14, 15, 16, 21, 22, 25, 26, 31, 32, 33, 34, 37, 38, 43, 44, 45, 46, 49, 50, 51, 52, 57, 58, 61, 62, 63, 64, 67, 68, 73, 74, 75, 76, 81, 82, 85, 86, 91, 92, 93, 94, 97, 98, 105, 106, 109, 110, 115, 116, 117, 118, 121, 122, 123
Offset: 1

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Author

Muniru A Asiru, Aug 04 2018

Keywords

Links

Crossrefs

Subsequence of A005100.
Numbers j such that both k and k + j are consecutive deficient numbers: this sequence (j=1), A317048 (j=2), A317049 (j=3).

Programs

  • GAP
    A:=Filtered([1..200],k->Sigma(k)<2*k);;
a:=List(Filtered([1..Length(A)-1],i->A[i+1]-A[i]=1),j->A[j]);
  • Maple
    A:=select(k->sigma(k)<2*k,[$1..200]): a:=seq(A[i],i in select(n->A[n+1]-A[n]=1,[$1..nops(A)-1]));
  • PARI
    isok(n) = (sigma(n) < 2*n) && (sigma(n+1) < 2*(n+1)); \\ Michel Marcus, Aug 20 2018

A317049 Numbers k such that both k and k + 3 are consecutive deficient numbers.

Original entry on oeis.org

5774, 5983, 7423, 11023, 21734, 21943, 26143, 27403, 39374, 43063, 49663, 56923, 58694, 61423, 69614, 70783, 76543, 77174, 79694, 81079, 81674, 82003, 84523, 84643, 89774, 91663, 98174, 103454, 104894, 106783, 109394, 111823, 116654, 116863, 120014, 121903
Offset: 1

Views

Author

Muniru A Asiru, Aug 04 2018

Keywords

Links

Crossrefs

Subsequence of A005100.
Numbers j such that both k and k + j are consecutive deficient numbers: A317047 (j=1), A317048 (j=2), this sequence (j=3).

Programs

  • GAP
    A:=Filtered([1..130000],k->Sigma(k)<2*k);;
a:=List(Filtered([1..Length(A)-1],i->A[i+1]-A[i]=3),j->A[j]);
  • Maple
    with(numtheory):  A:=select(k->sigma(k)<2*k,[$1..130000]):
a:=seq(A[i],i in select(k->A[k+1]-A[k]=3,[$1..nops(A)-1]));
  • Mathematica
    SequencePosition[Table[If[DivisorSigma[1,n]<2n,1,0],{n,122000}],{1,0,0,1}][[All,1]] (* Requires Mathematica version 10 or later *) (* Harvey P. Dale, May 28 2019 *)

A317045 Numbers k such that A(k+1) = A(k) + 2, where A() = A005100() are the deficient numbers.

Original entry on oeis.org

5, 10, 15, 16, 19, 22, 23, 28, 31, 32, 37, 42, 43, 46, 51, 54, 55, 60, 61, 64, 67, 68, 73, 76, 77, 78, 81, 84, 85, 90, 95, 100, 105, 106, 109, 114, 119, 122, 123, 128, 133, 134, 137, 142, 147, 150, 151, 152, 155, 158, 159, 164, 167, 168, 169, 172, 177, 182
Offset: 1

Views

Author

Muniru A Asiru, Aug 04 2018

Keywords

Links

Crossrefs

A317048 is the main sequence for this entry.
Numbers k such that A(k+1) = A(k) + j, where A() = A005100() are the deficient numbers: A317044 (j=1), this sequence (j=2), A317046 (k=3).
Cf. A005100, A125238.

Programs

  • GAP
    A:=Filtered([1..300],k->Sigma(k)<2*k);;  a:=Filtered([1..Length(A)-1],i->A[i+1]=A[i]+2);
  • Maple
    with(numtheory): A:=select(k->sigma(k)<2*k,[$1..300]):
 a:=select(j->A[j+1]=A[j]+2,[$1..nops(A)-1]);
  • Mathematica
    Position[Differences[Select[Range[250], DivisorSigma[1, #] < 2*# &]], 2] // Flatten (* Amiram Eldar, Mar 15 2024 *)

Formula

Sequence is { k | A005100(k+1) = A005101(k) + 2 }.
Sequence is { k | A125238(k) = 2 }.
Showing 1-3 of 3 results.

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

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