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.

A048948 Values of y in solutions to sigma(x^3)=y^2, where x are given by A008849.

Original entry on oeis.org

1, 20, 1292054400, 10927088640, 25841088000, 218541772800, 346787400960, 4084563974400, 4422275520000, 5977228233600, 6935748019200, 12161257680000, 14165346124800, 31925327616000, 50340380688000, 81691279488000, 51671470406400, 88445510400000
Offset: 1

Views

Author

Eric W. Weisstein

Keywords

Links

Crossrefs

Cf. A008849.

Extensions

Missing terms added by Donovan Johnson, Mar 10 2012

A008847 Numbers k such that sum of divisors of k^2 is a square.

Original entry on oeis.org

1, 9, 20, 180, 1306, 1910, 11754, 17190, 32486, 38423, 47576, 48202, 50920, 51590, 83884, 104855, 132682, 198534, 247863, 292374, 300876, 312374, 313929, 334330, 345807, 376095, 428184, 433818, 458280, 464310, 469623, 498892, 623615, 754956, 768460, 787127, 943695, 985369
Offset: 1

Views

Author

N. J. A. Sloane

Keywords

Comments

These are the square roots of squares in A006532. - M. F. Hasler, Oct 23 2010

References

  • A. H. Beiler, Recreations in the Theory of Numbers, Dover, NY, 1964, p. 10.
  • I. Kaplansky, The challenges of Fermat, Wallis and Ozanam (and several related challenges): II. Fermat's second challenge, Preprint, 2002.

Links

Crossrefs

Cf. A008848, A008849, A008850, A163763.
Cf. A000203, A010052, A000290.

Programs

  • Haskell
    a008847 n = a008847_list !! (n-1)
a008847_list = filter ((== 1) . a010052 . a000203 . a000290) [1..]
-- Reinhard Zumkeller, Mar 27 2013
  • Maple
    with(numtheory): readlib(issqr): for i from 1 to 10^5 do if issqr(sigma(i^2)) then print(i); fi; od;
  • Mathematica
    s = {}; Do[ If[IntegerQ[ Sqrt[ DivisorSigma[1, n^2]]], Print[n]; AppendTo[s, n]], {n, 10^6}]; s (* Jean-François Alcover, May 05 2011 *)
Select[Range[1000000],IntegerQ[Sqrt[DivisorSigma[1,#^2]]]&] (* Harvey P. Dale, Aug 22 2011 *)
  • PARI
    is_A008847(n)=issquare(sigma(n^2)) \\ M. F. Hasler, Oct 23 2010

Formula

A163763(n) = sqrt(sigma(A008847(n)^2)). - M. F. Hasler, Oct 16 2010
a(n) = sqrt(A008848(n)). - Zak Seidov, May 01 2016

A008850 Numbers n such that sum of divisors of n^2 is a cube.

Original entry on oeis.org

1, 43098, 20746664124, 21531558370, 25933330155, 30519275171, 453393100534, 803844998180, 1233758294601, 2358796315843, 6260406046762, 7339897643091, 7540242750903, 8532869860592, 11879890160946, 17538398093508
Offset: 1

Views

Author

N. J. A. Sloane

Keywords

References

  • A. H. Beiler, Recreations in the Theory of Numbers, Dover, NY, 1964, p. 9.
  • L. E. Dickson, History of the Theory of Numbers. Carnegie Institute Public. 256, Washington, DC, Vol. 1, 1919; Vol. 2, 1920; Vol. 3, 1923, see vol. 1, p. 54.
  • Julian Havil, Gamma, Exploring Euler's Constant, Princeton University Press, Princeton and Oxford, 2003, page 92.
  • I. Kaplansky, The challenges of Fermat, Wallis and Ozanam (and several related challenges): II. Fermat's second challenge, Preprint, 2002.

Links

Crossrefs

Cf. A008849.

Extensions

More terms from David W. Wilson (whose search was complete only through a(2) = 43098), Sep 15 1996
Kaplansky gives two further numbers with this property: 2597942466059820 and 6847610254216117540. The first is probably new and the second is in Dickson.
I. Kaplansky and Will Jagy have verified that there are no other terms below 9*10^11. - Oct 13 2002

A046872 F-primes.

Original entry on oeis.org

7, 47, 191, 239, 307, 463, 499, 701, 743, 787, 853, 1087, 1123, 1301, 1487, 1553, 1567, 1823, 2309, 2621, 2843, 2903, 3083, 3203, 3319, 3323, 3359, 3373, 3541, 3583, 3557, 3617, 3659, 3671, 3727, 3769, 3863, 3947, 4217, 4327, 4373, 4391
Offset: 1

Views

Author

N. J. A. Sloane, Oct 05 2002

Keywords

Comments

Call the numbers in A008849 F-numbers; then a prime p is called an F-prime if there exists a squarefree F-number q_1*q_2*...*q_r*p with q_1 < q_2 < ... < q_r < p in which the q_i's are primes but not F-primes.

References

  • I. Kaplansky, The challenges of Fermat, Wallis and Ozanam (and several related challenges): I. Fermat's first challenge, Preprint, 2002.

Crossrefs

Cf. A008849.
Showing 1-4 of 4 results.

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

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