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 1-6 of 6 results.

A048251 a(n) is the smallest number whose sum of divisors is 6^n.

Original entry on oeis.org

1, 5, 22, 102, 510, 3210, 17490, 112890, 600270, 3466470, 20205570, 118879530, 697118730, 3949737330, 24217298490, 143487592710, 841422307110, 4973562896610, 29520886859310, 180254162529210, 1052751138726210, 6301225298627490, 37854941354933010, 224270177470178070
Offset: 0

Views

Author

Labos Elemer

Keywords

Comments

Terms of this sequence are products of distinct terms in A005105. - Ray Chandler, Sep 01 2010

Examples

			sigma(k) = 1296 = 6^4 for each k in {510, 642, 710, 742, 782, 795, 862, 935, 1177, 1207, 1219}; the smallest of these is a(4)=510.

Links

Crossrefs

Cf. A006532, A020477, A019422, A019423, A018427, A048252-A048256.

Programs

  • PARI
    a(n) = {my(k=1); while (sigma(k) != 6^n, k++); k;} \\ Michel Marcus, May 14 2018

Formula

a(n) = Min{k : A000203(k) = 6^n}.

Extensions

a(9)-a(14) from Donovan Johnson, Sep 02 2008
a(15)-a(24) from Walter Kehowski, Aug 22 2010
Edited and extended by Ray Chandler, Sep 01 2010
Error in sequence corrected by N. J. A. Sloane, Oct 04 2010

A048257 Integers whose sum of divisors is a 7th power.

Original entry on oeis.org

1, 93, 127, 11811, 112890, 120054, 124338, 127330, 132770, 133998, 134090, 137058, 138754, 139962, 146710, 148665, 148810, 149534, 153986, 155510, 160215, 161194, 164985, 167134, 170986, 173098, 183687, 184682, 187143, 191913, 198485, 206823, 206965, 207687
Offset: 1

Views

Author

Labos Elemer

Keywords

Comments

If m and n are coprime members of the sequence, then m*n is also a member. - Robert Israel, May 10 2018

Examples

			Divisors(11811) = {1,3,31,93,127,381,3937,11811} and sigma(11811) = 16384 = 4^7.

Links

Crossrefs

Cf. A000203, A006532, A020477, A019422, A019423, A019424, A048251-A048256, A048258.

Programs

  • Maple
    filter:= n -> type(map(t -> t[2]/7, ifactors(numtheory:-sigma(n))[2]),list(integer)):
select(filter, [$1..21*10^4]); # Robert Israel, May 09 2018
  • Mathematica
    Select[Range[210000],IntegerQ[Surd[DivisorSigma[1,#],7]]&] (* Harvey P. Dale, Jun 09 2017 *)
  • PARI
    isok(n) = ispower(sigma(n), 7); \\ Michel Marcus, Dec 20 2013

Formula

sigma(a(n)) = x^7, where the initial values of x are 1, 2, 4, 6 (48 times), ...

A048252 Largest number whose sum of divisors is 6^n.

Original entry on oeis.org

1, 5, 22, 187, 1219, 7597, 46117, 278857, 1676377, 10067797, 60450517, 362758177, 2176626817, 13060193977, 78363525817, 470183516857, 2820894903487, 16926601754197, 101559860054047, 609359671998037, 3656158318966357
Offset: 0

Views

Author

Labos Elemer

Keywords

Comments

Terms of this sequence are products of distinct terms in A005105. - Ray Chandler, Sep 01 2010

Links

Crossrefs

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

Programs

  • PARI
    a(n) = {sn = 6^n; forstep(x=sn, 1, -1, if (sigma(x) == sn, return (x)););} \\ Michel Marcus, Dec 15 2013

Extensions

a(9)-a(14) from Donovan Johnson, Sep 02 2008
a(15)-a(20) from Donovan Johnson, Nov 22 2008
Edited and extended by Ray Chandler, Sep 01 2010

A048253 a(n) is the number of integers whose sum of divisors is 6^n.

Original entry on oeis.org

1, 1, 1, 5, 11, 18, 30, 48, 85, 148, 250, 415, 669, 1066, 1697, 2635, 4036, 6111, 9137, 13540, 19930, 29098, 42184, 60655, 86598, 122821, 173314, 243469, 340329, 473221, 654779, 901741, 1236668, 1689322, 2298592, 3115200, 4206016, 5658677, 7588039
Offset: 0

Views

Author

Labos Elemer

Keywords

Examples

			For n=3, sigma(1,k) = 6^3 = 216 for each of 5 integers: 102, 110, 142, 159, and 187, so a(3) = 5.

Links

Crossrefs

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

Programs

  • Mathematica
    With[{s = Array[DivisorSigma[1, #] &, 6^8]}, Array[Count[s, 6^#] &, Log[6, Length@ s] + 1, 0]] (* Michael De Vlieger, May 14 2018 *)
  • PARI
    a(n) = sum(k=1, 6^n, sigma(k)==6^n); \\ Michel Marcus, May 14 2018

Extensions

a(9)-a(14) from Donovan Johnson, Sep 02 2008
Edited and extended by Ray Chandler, Sep 01 2010

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

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 *)
Showing 1-6 of 6 results.

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