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.

A363298 Number of refactorable unitary divisors of n.

Original entry on oeis.org

1, 2, 1, 1, 1, 2, 1, 2, 2, 2, 1, 2, 1, 2, 1, 1, 1, 4, 1, 1, 1, 2, 1, 3, 1, 2, 1, 1, 1, 2, 1, 1, 1, 2, 1, 3, 1, 2, 1, 3, 1, 2, 1, 1, 2, 2, 1, 1, 1, 2, 1, 1, 1, 2, 1, 3, 1, 2, 1, 3, 1, 2, 2, 1, 1, 2, 1, 1, 1, 2, 1, 4, 1, 2, 1, 1, 1, 2, 1, 2, 1, 2, 1, 3, 1, 2, 1, 3, 1, 4
Offset: 1

Views

Author

Wesley Ivan Hurt, May 26 2023

Keywords

Crossrefs

Cf. A034444, A336041, A363085.

Programs

  • Mathematica
    a[n_] := DivisorSum[n, 1 &, CoprimeQ[#, n/#] && Divisible[#, DivisorSigma[0, #]] &]; Array[a, 100] (* Amiram Eldar, May 26 2023 *)

Formula

a(n) = Sum_{d|n, tau(d)|d, gcd(d,n/d)=1} 1.

A363091 Sum of the divisor complements of the refactorable unitary divisors of n.

Original entry on oeis.org

1, 3, 3, 4, 5, 9, 7, 9, 10, 15, 11, 13, 13, 21, 15, 16, 17, 30, 19, 20, 21, 33, 23, 28, 25, 39, 27, 28, 29, 45, 31, 32, 33, 51, 35, 41, 37, 57, 39, 46, 41, 63, 43, 44, 50, 69, 47, 48, 49, 75, 51, 52, 53, 81, 55, 64, 57, 87, 59, 66, 61, 93, 70, 64, 65, 99, 67, 68, 69, 105, 71
Offset: 1

Views

Author

Wesley Ivan Hurt, May 27 2023

Keywords

Crossrefs

Cf. A034444, A336041, A363085, A363298.

Programs

  • Mathematica
    a[n_] := n*DivisorSum[n, 1/# &, CoprimeQ[#, n/#] && Divisible[#, DivisorSigma[0, #]] &]; Array[a, 100]

Formula

a(n) = n * Sum_{d|n, tau(d)|d, gcd(d,n/d)=1} 1 / d.

A363318 Total distance from n to each of its refactorable unitary divisors.

Original entry on oeis.org

0, 1, 2, 3, 4, 9, 6, 7, 8, 17, 10, 11, 12, 25, 14, 15, 16, 42, 18, 19, 20, 41, 22, 39, 24, 49, 26, 27, 28, 57, 30, 31, 32, 65, 34, 62, 36, 73, 38, 71, 40, 81, 42, 43, 80, 89, 46, 47, 48, 97, 50, 51, 52, 105, 54, 103, 56, 113, 58, 107, 60, 121, 116, 63, 64, 129, 66, 67, 68, 137, 70
Offset: 1

Views

Author

Wesley Ivan Hurt, May 27 2023

Keywords

Crossrefs

Cf. A363085, A363298.

Programs

  • Mathematica
    a[n_] := DivisorSum[n, n - # &, CoprimeQ[#, n/#] && Divisible[#, DivisorSigma[0, #]] &]; Array[a, 100]

Formula

a(n) = Sum_{d|n, tau(d)|d, gcd(d,n/d)=1} (n - d).
a(n) = n * A363298(n) - A363085(n).
Showing 1-3 of 3 results.

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

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