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

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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;

A381548 Numbers k such that k and k+1 both have an odd number of abundant divisors.

Original entry on oeis.org

5984, 7424, 21735, 27404, 43064, 56924, 76544, 82004, 89775, 109395, 144584, 158235, 164835, 165375, 174824, 222704, 266475, 271215, 300104, 311024, 322335, 326655, 326864, 334304, 347984, 350175, 371924, 387584, 393855, 414315, 442035, 445004, 447524, 477224
Offset: 1

Views

Author

Amiram Eldar, Feb 26 2025

Keywords

Comments

Numbers k such that k and k+1 are both in A381546.

Examples

			5984 is a term since it has 9 abundant divisors (88, 176, 272, 352, 544, 748, 1496, 2992, 5984) and 5984 + 1 = 5985 has one abundant divisor (5985 itself).
21735 is a term since it has 3 abundant divisors (945, 7245, 21735) and 21735 + 1 = 21736 has 9 abundant divisors (88, 104, 572, 836, 1144, 1672, 1976, 10868, 21736).

Links

Crossrefs

Subsequence of A096399 and A381546.
Subsequences: A381549.

Programs

  • Mathematica
    q[n_] := q[n] = OddQ[DivisorSum[n, 1 &, DivisorSigma[-1, #] > 2 &]]; Select[Range[500000], q[#] && q[#+1] &]
  • PARI
    is1(k) = sumdiv(k, d, (sigma(d, -1) > 2)) % 2;
list(lim) = forstep(k = 3, lim, 2, if(is1(k), if(is1(k-1), print1(k-1, ", ")); if(is1(k+1), print1(k, ", "))));

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);
Showing 1-3 of 3 results.

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

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