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.

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A048255 Integers whose sum of divisors is 6^5 = 7776.

Original entry on oeis.org

3210, 3498, 3710, 3882, 3910, 4310, 4922, 4982, 5182, 5457, 5885, 6035, 6095, 6307, 6797, 7117, 7327, 7597
Offset: 1

Views

Author

Labos Elemer

Keywords

Comments

Sequence has A048253(5)=18 terms from A048251(5)=3210 to A048252(5)=7597. - Ray Chandler

Examples

			Divisors of 7597 are {1,71,107,7597}, whose sum is 7776, so 7597 is in the sequence.

Crossrefs

Cf. A006532, A020477, A019422, A019423, A018427, A048251-A048256.

Programs

  • Mathematica
    Select[Range[7600],DivisorSigma[1,#]==7776&] (* Harvey P. Dale, Jun 04 2016 *)
  • PARI
    for(i=1,t=6^5, sigma(i)==t & print1(i",")) \\ M. F. Hasler, Dec 09 2009

Formula

A048255 = { n | A000203(n)=6^5 }. - M. F. Hasler, Dec 09 2009

Extensions

Minor edits, keywords added, and values checked with given PARI code by M. F. Hasler, Dec 09 2009

A334353 Least positive integer m relatively prime to n such that sigma(m*n) is a fourth power, where sigma(k) is the sum of the divisors of k.

Original entry on oeis.org

1, 255, 170, 3783, 102, 85, 31, 39063, 34711, 51, 85, 1261, 1164, 53, 34, 417067, 30, 716125, 499, 55563, 127, 345, 34, 13021, 417067, 55563, 3493, 117273, 10776, 17, 7, 34359, 230, 15, 321, 10549987, 2469230, 13021, 388, 8483, 28128, 187, 5323, 30865, 314758, 17, 230, 1345225, 1481538, 9473379, 10, 291, 14, 82445, 17, 60615, 1999, 7495, 5960, 18521
Offset: 1

Views

Author

Zhi-Wei Sun, Apr 24 2020

Keywords

Comments

Conjecture: For any positive integers k and m, there is a positive integer n relatively prime to m such that sigma(m*n) is a k-th power.
This implies that a(n) exists for every n = 1,2,3,....
See also A334350 for a similar conjecture involving Euler's totient function (A000010).

Examples

			a(2) = 255 with gcd(2, 255) = 1 and sigma(2*255) = sigma(2)*sigma(255) = 3*432 = 1296 = 6^4.
a(64) = 1851519543 with gcd(64, 1851519543) = 1 and sigma(64*1851519543) = sigma(64)*sigma(1851519543) = 127*2654704368 = 337147454736 = 762^4.

Links

Crossrefs

Cf. A000010, A000203, A000583, A006532, A019422, A020477, A334350.

Programs

  • Mathematica
    QQ[n_]:=QQ[n]=IntegerQ[n^(1/4)];
sigma[n_]:=sigma[n]=DivisorSigma[1,n];
tab={};Do[m=0;Label[aa];m=m+1;If[GCD[m,n]==1&&QQ[sigma[m]*sigma[n]],tab=Append[tab,m],Goto[aa]],{n,1,60}];tab
  • PARI
    a(n) = my(m=1,s=sigma(n)); while (!((gcd(n, m) == 1) && ispower(s*sigma(m), 4)), m++); m; \\ Michel Marcus, Apr 25 2020

A048254 Numbers whose sum of divisors is 6^4 = 1296.

Original entry on oeis.org

510, 642, 710, 742, 782, 795, 862, 935, 1177, 1207, 1219
Offset: 1

Views

Author

Labos Elemer

Keywords

Comments

Sequence has A048253(4)=11 terms from A048251(4)=510 to A048252(4)=1219. - Ray Chandler, Sep 01 2010

Examples

			The divisors of 1219 are 1, 23, 53, and 1219, whose sum is 1296, so 1219 is in the sequence.

Crossrefs

Cf. A006532, A020477, A019422, A019423, A018427, A048251-A048256.

Programs

  • Mathematica
    Select[Range[6^4], DivisorSigma[1, # ] == 6^4 &] (* Ray Chandler, Sep 01 2010 *)
Previous Showing 11-13 of 13 results.

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

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