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).

A356453 Numbers k such that 2*k^2 is not in A014567; complement of A356449.

Original entry on oeis.org

3, 6, 9, 10, 12, 15, 18, 21, 24, 27, 28, 30, 33, 36, 39, 40, 42, 45, 48, 50, 51, 54, 57, 60, 63, 66, 69, 70, 72, 75, 77, 78, 81, 84, 87, 90, 93, 96, 99, 102, 105, 108, 110, 111, 114, 117, 120, 123, 126, 129, 130, 132, 133, 135, 136, 138, 140, 141, 144, 147, 150, 153, 154, 155
Offset: 1

Views

Author

Jianing Song, Aug 07 2022

Keywords

Comments

Numbers k such that k and sigma(2*k^2) are not coprime, sigma = A000203.
Includes all multiples of 3 since 3 divides sigma(m) if m is twice a square (cf. A065766).

Examples

			10 is a term since 10 and sigma(2*10^2) = 465 have a common factor 5.

Links

Crossrefs

Cf. A014567, A000203, A356448, A356449, A356452, A356454, A356456 (all multiples of 3 removed), A065766.

Programs

  • Mathematica
    Select[Range[155],GCD[#, DivisorSigma[1,2#^2]]>1 &] (* Stefano Spezia, Aug 07 2024 *)
  • PARI
    isA356453(n) = gcd(n, sigma(2*n^2))>1

A356454 Numbers k such that 4*k^2 is not in A014567; complement of A356451.

Original entry on oeis.org

7, 21, 35, 39, 42, 49, 56, 57, 62, 63, 77, 78, 84, 91, 93, 99, 105, 111, 114, 117, 119, 126, 129, 133, 147, 154, 155, 156, 161, 168, 171, 175, 183, 186, 189, 195, 198, 201, 203, 209, 210, 217, 219, 222, 228, 231, 234, 237, 245, 252, 258, 259, 266, 273, 275, 279, 280, 285
Offset: 1

Views

Author

Jianing Song, Aug 07 2022

Keywords

Comments

Numbers k such that k and sigma(4*k^2) are not coprime, sigma = A000203.

Examples

			7 is a term since 7 and sigma(4*7^2) = 399 have a common factor 7.

Links

Crossrefs

Cf. A014567, A000203, A356448, A356452, A356453.

Programs

  • PARI
    isA356454(n) = gcd(n, sigma(4*n^2))>1

Formula

a(n) = A356452(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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