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.

A228962 Smallest sets of 5 consecutive abundant numbers in arithmetic progression. The initial abundant number is listed.

Original entry on oeis.org

114, 228, 234, 582, 654, 1002, 1008, 1242, 1248, 1254, 1542, 1794, 1908, 2094, 2214, 2262, 2328, 2334, 2502, 2634, 2754, 2988, 3054, 3102, 3348, 3354, 3642, 4182, 4188, 4314, 4362, 4368, 4428, 4434, 4482, 4728, 4788, 4902, 5202, 5208, 5268, 5274, 5742, 5862
Offset: 1

Views

Author

Shyam Sunder Gupta, Nov 10 2013

Keywords

Examples

			114, 120, 126, 132, 138 is the smallest set of 5 consecutive abundant numbers in arithmetic progression so 114 is in the list.

Links

Crossrefs

Cf. A005101, A228433, A228844, A228961.

Programs

  • Mathematica
    AbundantQ[n_] := DivisorSigma[1, n] > 2 n; m = 2; z1 = 18; cd = 6; a = {}; Do[If[AbundantQ[n], If[n - z1 == cd, m = m + 1; If[m > 4, AppendTo[a, n - 4*cd]], m = 2; cd = n - z1]; z1 = n], {n, 19, 1000000}]; a

A231625 Smallest sets of 4 consecutive deficient numbers in arithmetic progression. The initial deficient number is listed.

Original entry on oeis.org

1, 2, 7, 8, 13, 14, 31, 32, 43, 44, 49, 50, 61, 62, 73, 74, 91, 92, 99, 115, 116, 121, 122, 127, 128, 133, 134, 145, 146, 151, 152, 163, 164, 169, 170, 181, 182, 187, 188, 195, 211, 212, 219, 229, 230, 235, 236, 241, 242, 247, 248, 253, 254, 265, 266, 283
Offset: 1

Views

Author

Shyam Sunder Gupta, Nov 11 2013

Keywords

Examples

			1, 2, 3, 4 is the smallest set of 4 consecutive deficient numbers in arithmetic progression so 1 is in the list.

Links

Crossrefs

Cf. A005100, A231623, A228961, A231624.

Programs

  • Mathematica
    DefQ[n_] := DivisorSigma[1, n] < 2 n; m = 2; z1 = 2; cd = 1; a = {}; Do[If[DefQ[n], If[n - z1 == cd, m = m + 1; If[m > 3, AppendTo[a, n - 3*cd]], m = 2; cd = n - z1]; z1 = n], {n, 3, 1000000}]; a

A228963 Smallest sets of 6 consecutive abundant numbers in arithmetic progression. The initial abundant number is listed.

Original entry on oeis.org

228, 1002, 1242, 1248, 2328, 3348, 4182, 4362, 4428, 5202, 5268, 6702, 6708, 6882, 7962, 7968, 8142, 8382, 8982, 9822, 9888, 10242, 11568, 11922, 11988, 12162, 12168, 12588, 13248, 13422, 13842, 13848, 14022, 14088, 14508, 15282, 15522, 15528, 16362, 16368
Offset: 1

Views

Author

Shyam Sunder Gupta, Nov 10 2013

Keywords

Examples

			228, 234, 240, 246, 252, 258 is the smallest set of 6 consecutive abundant numbers in arithmetic progression so 228 is in the list.

Links

Crossrefs

Cf. A005101, A228433, A228844, A228961, A228962.

Programs

  • Mathematica
    AbundantQ[n_] := DivisorSigma[1, n] > 2 n; m = 2; z1 = 18; cd = 6; a = {}; Do[If[AbundantQ[n], If[n - z1 == cd, m = m + 1; If[m > 5, AppendTo[a, n - 5*cd]], m = 2; cd = n - z1]; z1 = n], {n, 19, 1000000}]; a

A228964 Smallest sets of 7 consecutive abundant numbers in arithmetic progression. The initial abundant number is listed.

Original entry on oeis.org

1242, 6702, 7962, 12162, 13842, 15522, 16362, 18042, 18882, 19722, 24762, 26442, 27282, 27702, 28122, 28962, 36942, 38202, 39462, 43662, 44922, 45762, 48282, 48702, 51222, 55842, 56682, 60042, 62562, 63402, 66762, 69282, 69702, 70962, 71802, 73062, 73482
Offset: 1

Views

Author

Shyam Sunder Gupta, Nov 10 2013

Keywords

Examples

			1242, 1248, 1254, 1260, 1266, 1272, 1278 is the smallest set of 7 consecutive abundant numbers in arithmetic progression so 1242 is in the list.

Links

Crossrefs

Cf. A005101, A228433, A228844, A228961, A228962, A228963.

Programs

  • Mathematica
    AbundantQ[n_] := DivisorSigma[1, n] > 2 n; m = 2; z1 = 18; cd = 6; a = {}; Do[If[AbundantQ[n], If[n - z1 == cd, m = m + 1; If[m > 6, AppendTo[a, n - 6*cd]], m = 2; cd = n - z1]; z1 = n], {n, 19, 1000000}]; a
Select[Partition[Select[Range[80000],DivisorSigma[1,#]>2#&],7,1], Length[ Union[ Differences[#]]] ==1&][[All,1]] (* Harvey P. Dale, Oct 15 2017 *)

A228965 Smallest sets of 8 consecutive abundant numbers in arithmetic progression. The initial abundant number is listed.

Original entry on oeis.org

221355126, 402640540, 668862580, 739577140
Offset: 1

Views

Author

Shyam Sunder Gupta, Nov 10 2013

Keywords

Comments

Is this a duplicate of A231093? - R. J. Mathar, Nov 15 2013
No; there is some element of this sequence not in A231093 below approximately 10^10^72. In fact A228965 \ A231093 has positive lower density (though presumably quite small). Capsule proof: choose n such that an appropriately large number of primes divide n, n+1, ..., n+7. Since the reciprocal of the primes diverges, you can get sigma(n+i)/(n+i) arbitrarily large. - Charles R Greathouse IV, Nov 15 2013

Examples

			221355126, 221355128, 221355130, 221355132, 221355134, 221355136, 221355138, 221355140  is the smallest set of 8 consecutive abundant numbers in arithmetic progression so 221355126 is in the list.

Crossrefs

Cf. A005101, A228433, A228844, A228961, A228962, A228963, A228964.

Programs

  • Mathematica
    AbundantQ[n_] := DivisorSigma[1, n] > 2 n; m = 2; z1 = 18; cd = 6; a = {}; Do[If[AbundantQ[n], If[n - z1 == cd, m = m + 1; If[m > 7, AppendTo[a, n - 7*cd]], m = 2; cd = n - z1]; z1 = n], {n, 19, 1000000000}]; a
Showing 1-5 of 5 results.

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