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.

A136479 Odd primitive abundant numbers n such that n = x^2 + x + y^2 with y^2 < 2*x and x and y primes, subsequence of A136476.

Original entry on oeis.org

9555, 51765, 17787315
Offset: 1

Views

Author

Pierre CAMI, Dec 31 2007

Keywords

Comments

x values in A136477.

Examples

			9555 = 97^2+97+7^2 and 9555 odd primitive abundant number A136476(1), 97 and 7 primes so A136479(1) = 9555.

Crossrefs

Cf. A006038, A136476, A136477, A136478.

A136477 Numbers x such that for some y < sqrt(2x), x^2 + x + y^2 is an odd primitive abundant number, A136476(n).

Original entry on oeis.org

97, 112, 122, 135, 144, 179, 202, 207, 214, 217, 227, 354, 359, 477, 507, 569, 612, 632, 639, 732, 832, 2124, 2359, 2362, 2440, 2466, 2517, 2970, 3097, 3247, 3342, 3367, 3374, 3419, 3425, 3518, 3545, 3562, 3644, 3672, 3699, 3789, 3879, 3969, 3985, 4050
Offset: 1

Views

Author

Pierre CAMI, Dec 31 2007

Keywords

Comments

The corresponding y-values are listed in A136478. (Unlike the x-values listed here, y is not increasing with A136476(n).)

Examples

			97^2 + 97 + 7^2 = 9555 = A136476(1) is an odd primitive abundant number, so a(1) = 97.

Crossrefs

Cf. A006038, A136476, A136478, A136479.

Programs

  • PARI
    is(x,n=x^2+x+1,f)={forstep(y=1,sqrtint(2*x),2, sigma(n+=y*4-4,-1)>2 || next; for(i=1, #f=factor(n)[,1], sigma(n\f[i], -1)>2 && next(2)); return(1))} \\ M. F. Hasler, Feb 22 2017

Extensions

Edited by M. F. Hasler, Feb 22 2017

A136478 Smallest y such that for x = A136477(n), x^2 + x + y^2 is an odd primitive abundant number, A136476(n).

Original entry on oeis.org

7, 7, 3, 15, 15, 15, 7, 3, 5, 7, 3, 15, 15, 27, 3, 15, 3, 27, 15, 27, 13, 3, 49, 17, 55, 27, 27, 15, 53, 77, 63, 77, 15, 45, 15, 69, 45, 77, 15, 57, 75, 27, 75, 63, 55, 75, 49, 85, 7, 3
Offset: 1

Views

Author

Pierre CAMI, Dec 31 2007

Keywords

Comments

See A136477 and A136476 for the x-values and the abundant numbers x^2 + x + y^2.

Examples

			97^2+97+7^2 = 9555 = A136476(1) is an odd primitive abundant number, therefore a(1) = 7.

Crossrefs

Cf. A006038, A136476, A136477, A136479.

Programs

  • PARI
    {for(x=1, 5000, my(n=x^2+x+1, f); forstep(y=1, sqrtint(2*x), 2, sigma(n+=y*4-4, -1)>2 || next; for(i=1, #f=factor(n)[, 1], sigma(n\f[i], -1)>2 && next(2)); print1(y","); break))} \\ M. F. Hasler, Feb 22 2017

Formula

a(n) = sqrt(A136476(n) - A136477(n)^2 - A136477(n)). - M. F. Hasler, Feb 22 2017

Extensions

Edited by M. F. Hasler, Feb 22 2017
Showing 1-3 of 3 results.

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

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