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 1-4 of 4 results.

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

A356452 Even numbers k such that k^2 is not in A014567; complement of A356448 in the even numbers.

Original entry on oeis.org

14, 42, 70, 78, 84, 98, 112, 114, 124, 126, 154, 156, 168, 182, 186, 198, 210, 222, 228, 234, 238, 252, 258, 266, 294, 308, 310, 312, 322, 336, 342, 350, 366, 372, 378, 390, 396, 402, 406, 418, 420, 434, 438, 444, 456, 462, 468, 474, 490, 504, 516, 518, 532, 546, 550, 558
Offset: 1

Views

Author

Jianing Song, Aug 07 2022

Keywords

Comments

Even numbers k such that k and sigma(k^2) are not coprime, sigma = A000203.

Examples

			14 is a term since 14 and sigma(14^2) = 399 have a common factor 7.

Links

Crossrefs

Cf. A014567, A000203, A356448, A356453, A356454.

Programs

  • Mathematica
    Select[2 Range[300],!CoprimeQ[#,DivisorSigma[1,#^2]]&] (* Harvey P. Dale, Mar 09 2023 *)
  • PARI
    isA356452(n) = !(n%2) && gcd(n, sigma(n^2))>1

Formula

a(n) = 2*A356454(n).

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.

A356456 Numbers k not divisible by 3 such that 2*k^2 is not in A014567.

Original entry on oeis.org

10, 28, 40, 50, 70, 77, 110, 130, 133, 136, 140, 154, 155, 160, 161, 170, 176, 190, 196, 200, 209, 224, 230, 250, 259, 266, 275, 280, 290, 308, 310, 322, 350, 364, 370, 371, 377, 385, 410, 416, 418, 430, 440, 469, 470, 476, 490, 496, 518, 520, 530, 532, 539, 550, 553, 590
Offset: 1

Views

Author

Jianing Song, Aug 07 2022

Keywords

Comments

Numbers k not divisible by 3 such that k and sigma(2*k^2) are not coprime, sigma = A000203.
Note that if m is twice a square, then sigma(m) is divisible by 3 (cf. A065766).

Examples

			28 is a term since 28 and sigma(2*28^2) = 3591 have a common factor 7, and 28 is not divisible by 3.

Links

Crossrefs

Cf. A014567, A000203, A065766.
Equals A356453 \ A008585.

Programs

  • PARI
    isA356456(n) = (n%3) && gcd(n, sigma(2*n^2))>1
Showing 1-4 of 4 results.

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