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.

A046678 Number of divisors of n and sum of divisors of n are relatively prime.

Original entry on oeis.org

1, 2, 4, 8, 9, 16, 25, 36, 64, 81, 100, 121, 128, 144, 162, 225, 256, 289, 324, 400, 484, 512, 529, 576, 625, 729, 841, 900, 1024, 1089, 1156, 1250, 1296, 1458, 1600, 1681, 1936, 2025, 2116, 2209, 2304, 2401, 2500, 2601, 2809, 3025, 3364, 3481
Offset: 1

Views

Author

Labos Elemer

Keywords

Comments

It can be shown that this is a subsequence of A028982.

Links

Crossrefs

Cf. A000005, A000203, A028982, A046679, A046680, A046681, A046683, A046685.

Programs

  • Mathematica
    Select[Range[3490], CoprimeQ[DivisorSigma[1, #], DivisorSigma[0, #]] &] (* Jayanta Basu, Jun 27 2013 *)
  • PARI
    isok(n) = gcd(sigma(n), numdiv(n)) == 1; \\ Michel Marcus, Sep 24 2019

A046679 Numbers k such that the number of divisors of k and sum of squares of divisors of k are relatively prime.

Original entry on oeis.org

1, 2, 8, 9, 16, 18, 64, 72, 81, 128, 144, 625, 729, 1024, 1152, 1296, 1458, 2401, 4096, 5184, 5625, 5832, 6561, 8192, 9216, 10000, 11664, 13122, 15625, 21609, 28561, 31250, 32768, 38416, 40000, 46656, 50625, 52488, 59049, 65536, 83521, 90000
Offset: 1

Views

Author

Labos Elemer

Keywords

Comments

It can be shown that this is a subsequence of A028982.

Links

Crossrefs

Cf. A028982, A046678, A046680, A046681, A046683, A046685.

Programs

  • Mathematica
    Select[Range[91000],CoprimeQ[DivisorSigma[0,#], DivisorSigma[2,#]]&] (* Harvey P. Dale, May 11 2011 *)
  • PARI
    isok(n) = gcd(sigma(n, 2), numdiv(n)) == 1; \\ Michel Marcus, Sep 24 2019

Extensions

a(1)=1 added by Amiram Eldar, Sep 24 2019

A046680 Numbers k such that the number of divisors of k and sum of cubes of divisors of k are relatively prime.

Original entry on oeis.org

1, 2, 4, 8, 9, 16, 25, 36, 81, 100, 121, 128, 144, 162, 225, 256, 289, 324, 400, 484, 512, 529, 625, 729, 841, 900, 1024, 1089, 1156, 1250, 1296, 1458, 1681, 1936, 2025, 2116, 2209, 2304, 2401, 2500, 2601, 2809, 2916, 3025, 3364, 3481, 3600, 4096, 4356, 4624
Offset: 1

Views

Author

Labos Elemer

Keywords

Comments

It can be shown that this is a subsequence of A028982.

Links

Crossrefs

Cf. A028982, A046678, A046679, A046681, A046683, A046685.

Programs

  • Mathematica
    Select[Range[5000], CoprimeQ[DivisorSigma[0, #], DivisorSigma[3, #]] &] (* Amiram Eldar, Aug 08 2019 *)
  • PARI
    isok(n) = gcd(numdiv(n), sigma(n, 3)) == 1; \\ Michel Marcus, Sep 24 2019

A046683 Numbers k such that the sum of squares of divisors of k and sum of cubes of divisors of k are relatively prime.

Original entry on oeis.org

1, 2, 4, 9, 18, 25, 36, 100, 121, 225, 289, 484, 529, 841, 900, 1089, 1156, 1681, 2116, 2209, 2601, 2809, 3364, 3481, 4356, 4761, 5041, 6724, 6889, 7225, 7569, 7921, 8836, 10201, 10404, 11236, 11449, 12769, 13225, 13924, 15129, 17161, 18769, 19044
Offset: 1

Views

Author

Labos Elemer

Keywords

Comments

It can be shown that this is a subsequence of A028982.

Links

Crossrefs

Cf. A028982, A046678, A046679, A046680, A046681, A046685.

Programs

  • Mathematica
    sdcdQ[n_]:=Module[{d=Divisors[n]},CoprimeQ[Total[d^2],Total[d^3]]]; Select[ Range[ 20000],sdcdQ] (* Harvey P. Dale, Apr 09 2018 *)
  • PARI
    isok(n) = gcd(sigma(n, 2), sigma(n, 3)) == 1; \\ Michel Marcus, Sep 24 2019

A046685 Numbers k such that the sum of cubes of divisors of k and the sum of 4th powers of divisors of k are relatively prime.

Original entry on oeis.org

1, 2, 4, 8, 9, 18, 25, 100, 121, 225, 289, 484, 529, 841, 1089, 1156, 1681, 2116, 2209, 2601, 2809, 3364, 3481, 4761, 5041, 6724, 6889, 7225, 7569, 7921, 8836, 10201, 11236, 11449, 12769, 13225, 13924, 15129, 17161, 18769, 19881, 20164, 21025
Offset: 1

Views

Author

Labos Elemer

Keywords

Comments

It can be shown that this is a subsequence of A028982.
From Robert Israel, Jul 09 2018: (Start)
The only terms that are not in A062503 are 2, 8 and 18.
No term is divisible by a term of A002476.
p^2 is a term for every p in A003627. (End)

Links

Crossrefs

Cf. A002476, A003627, A028982, A046678, A046679, A046680, A046681, A046683, A062503.

Programs

  • Maple
    N:= 10^6: # to get all terms <= N
sort(select(filter, [seq(t^2,t=1..isqrt(N)),seq(2*t^2,t=1..isqrt(N/2))])); # Robert Israel, Jul 09 2018
  • Mathematica
    Select[Range[25000], CoprimeQ[DivisorSigma[3, #], DivisorSigma[4, #]] &] (* Michael De Vlieger, Aug 10 2023 *)
  • PARI
    isok(n) = gcd(sigma(n, 3), sigma(n, 4)) == 1; \\ Michel Marcus, Sep 24 2019

A046659 Numbers whose sum of divisors and sum of cubes of divisors are relatively prime.

Original entry on oeis.org

1, 4, 9, 25, 36, 100, 121, 225, 289, 484, 529, 841, 900, 1089, 1156, 1681, 2116, 2209, 2601, 2809, 3364, 3481, 4356, 4761, 5041, 6724, 6889, 7225, 7569, 7921, 8836, 10201, 10404, 11236, 11449, 12769, 13225, 13924, 15129, 17161, 18769, 19044
Offset: 1

Views

Author

Labos Elemer

Keywords

Comments

It appears that (a) all the numbers are squares, (b) the number of divisors is a power of 3.
It can be shown that this is a subset of A028982.

Examples

			k=100 has 9 divisors whose sum is 217 = 7*31 and whose sum of cubes is 1149823 = 19*73*829; gcd(217, 1149823) = 1, so 100 is in the sequence.

Links

Crossrefs

Cf. A028982, A046679, A046680, A046681, A046683, A046685.

Programs

  • Mathematica
    Select[Range[20000],GCD[DivisorSigma[1,#],DivisorSigma[3,#]]==1&]  (* Harvey P. Dale, Feb 19 2011 *)
  • PARI
    isok(n) = gcd(sigma(n), sigma(n, 3)) == 1; \\ Michel Marcus, May 14 2018
Showing 1-6 of 6 results.

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

Content is available under The OEIS End-User License Agreement.