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.

A356448 Even numbers k such that k^2 is in A014567.

Original entry on oeis.org

2, 4, 6, 8, 10, 12, 16, 18, 20, 22, 24, 26, 28, 30, 32, 34, 36, 38, 40, 44, 46, 48, 50, 52, 54, 56, 58, 60, 62, 64, 66, 68, 72, 74, 76, 80, 82, 86, 88, 90, 92, 94, 96, 100, 102, 104, 106, 108, 110, 116, 118, 120, 122, 128, 130, 132, 134, 136, 138, 140, 142, 144, 146, 148
Offset: 1

Views

Author

Jianing Song, Aug 07 2022

Keywords

Comments

Even numbers k such that k and sigma(k^2) are coprime, sigma = A000203.

Examples

			12 is a term since 12 and sigma(12^2) = 403 are coprime.

Links

Crossrefs

Cf. A014567, A000203, A356382, A356449, A356451, A356452 (complement in the even numbers).

Programs

  • PARI
    isA356448(n) = !(n%2) && gcd(n,sigma(n^2))==1

Formula

a(n) = 2*A356451(n).

A356449 Numbers k such that 2*k^2 is in A014567.

Original entry on oeis.org

1, 2, 4, 5, 7, 8, 11, 13, 14, 16, 17, 19, 20, 22, 23, 25, 26, 29, 31, 32, 34, 35, 37, 38, 41, 43, 44, 46, 47, 49, 52, 53, 55, 56, 58, 59, 61, 62, 64, 65, 67, 68, 71, 73, 74, 76, 79, 80, 82, 83, 85, 86, 88, 89, 91, 92, 94, 95, 97, 98, 100, 101, 103, 104, 106, 107, 109, 112, 113
Offset: 1

Views

Author

Jianing Song, Aug 07 2022

Keywords

Comments

Numbers k such that k and sigma(2*k^2) are coprime, sigma = A000203.
No term can be a multiple of 3 since 3 divides sigma(m) if m is twice a square (cf. A065766).

Examples

			20 is a term since 20 and sigma(2*20^2) = 1953 are coprime.

Links

Crossrefs

Cf. A014567, A000203, A356382, A356448, A356451, A356453 (complement), A065766.

Programs

  • PARI
    isA356449(n) = gcd(n,sigma(2*n^2))==1

A356451 Numbers k such that 4*k^2 is in A014567.

Original entry on oeis.org

1, 2, 3, 4, 5, 6, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 36, 37, 38, 40, 41, 43, 44, 45, 46, 47, 48, 50, 51, 52, 53, 54, 55, 58, 59, 60, 61, 64, 65, 66, 67, 68, 69, 70, 71, 72, 73, 74, 75, 76, 79, 80, 81, 82, 83
Offset: 1

Views

Author

Jianing Song, Aug 07 2022

Keywords

Comments

Numbers k such that k and sigma(4*k^2) are coprime, sigma = A000203.

Examples

			12 is a term since 12 and sigma(4*12^2) = 1651 are coprime.

Links

Crossrefs

Cf. A014567, A000203, A356382, A356448, A356449, A356454 (complement).

Programs

  • PARI
    isA356450(n) = gcd(n,sigma(4*n^2))==1

Formula

a(n) = A356448(n)/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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