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.

A381546 Numbers with an odd number of abundant divisors.

Original entry on oeis.org

12, 18, 20, 30, 36, 42, 48, 56, 66, 70, 72, 78, 80, 84, 88, 90, 102, 104, 108, 114, 120, 126, 132, 138, 140, 144, 156, 162, 174, 186, 192, 196, 198, 204, 222, 224, 228, 234, 246, 252, 258, 270, 272, 276, 282, 288, 300, 304, 306, 308, 318, 320, 324, 330, 336, 342, 348
Offset: 1

Views

Author

Amiram Eldar, Feb 26 2025

Keywords

Comments

Numbers k such that A080224(k) is odd.
The primitive abundant numbers (A091191) are all terms of this sequence since A080224(A091191(n)) = 1 for all n.

Examples

			12 is a term since it has only one abundant divisor, 12 itself.
36 is a term since it has 3 abundant divisors, 12, 18 and 36.
72 is a term since it has 5 abundant divisors, 12, 18, 24, 36 and 72.

Links

Crossrefs

Cf. A080224.
Subsequence of A005101.
Subsequences: A091191, A381547, A381548, A381549.

Programs

  • Mathematica
    q[n_] := OddQ[DivisorSum[n, 1 &, DivisorSigma[-1, #] > 2 &]]; Select[Range[350], q]
  • PARI
    isok(k) = sumdiv(k, d, (sigma(d, -1) > 2)) % 2;

A381547 Odd numbers with an odd number of abundant divisors.

Original entry on oeis.org

945, 1575, 2205, 3465, 4095, 4725, 5355, 5775, 5985, 6435, 6615, 6825, 7245, 7425, 8085, 8415, 8505, 8925, 9135, 9555, 9765, 10395, 11025, 11655, 12285, 12705, 12915, 13545, 14175, 14805, 15015, 16065, 16695, 17955, 18585, 19215, 19635, 19845, 21105, 21735, 21945
Offset: 1

Views

Author

Amiram Eldar, Feb 26 2025

Keywords

Comments

Odd numbers k such that A080224(k) is odd.
Also, odd numbers with an odd sum of abundant divisors.
The odd primitive abundant numbers (A006038) are all terms of this sequence since A080224(A006038(n)) = 1 for all n.

Examples

			945 is a term since it is odd, and it has only one abundant divisor, 945 itself.
4725 is a term since it is odd, and it has 3 abundant divisors, 945, 1575 and 4725.
14175 is a term since it is odd, and it has 5 abundant divisors, 945, 1575, 2835, 4725 and 14175.

Links

Crossrefs

Cf. A080224, A187795.
Intersection of A005408 and A381546.
Subsequence of A005231.
Subsequences: A006038, A381548, A381549.

Programs

  • Mathematica
    q[n_] := OddQ[DivisorSum[n, 1 &, DivisorSigma[-1, #] > 2 &]]; Select[Range[1, 22000, 2], q]
  • PARI
    isok(k) = if(k % 2, sumdiv(k, d, (sigma(d, -1) > 2)) % 2, 0);

A381549 Numbers k such that k, k+1 and k+2 all have an odd number of abundant divisors.

Original entry on oeis.org

96236031968, 229687160624, 274957745984, 331240852304, 363015363248, 386136575824, 407374391150, 623810538350, 734609097584, 745885389248, 1080953007848
Offset: 1

Views

Author

Amiram Eldar, Feb 26 2025

Keywords

Comments

a(11) > 10^12, if it exists.

Examples

			96236031968 is a term since it has 7 abundant divisors (992, 512368, 1024736, 46580848, 93161696, 48118015984, 96236031968), 96236031968 + 1 = 96236031969 has 9 abundant divisors (7857927, 10025631, 12641013, 290743299, 2600973837, 3318483861, 4184175303, 5660943057, 96236031969), and 96236031968 + 2 = 96236031970 has one abundant divisor (96236031970 itself).

Crossrefs

Subsequence of A096536, A381546 and A381548.

Programs

  • Mathematica
    q[n_] := q[n] = OddQ[DivisorSum[n, 1 &, DivisorSigma[-1, #] > 2 &]]; With[{v = Import["https://oeis.org/A096536/b096536.txt", "Table"][[;; , 2]]}, Select[v, q[#] && q[# + 1] && q[# + 2] &]]

Extensions

a(11) from Jinyuan Wang, Mar 12 2025
Showing 1-3 of 3 results.

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

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