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.

A164646 Numbers n such that sigma(n)/phi(n) = 9/4.

Original entry on oeis.org

51, 477, 595, 3567, 17765, 20735, 41615, 104931, 276651, 470721, 493493, 599169, 834591, 993395, 1092845, 1242505, 1318521, 1479981, 1490645, 1712037, 2344045, 2736305, 2912463, 2986941, 2990709, 3042873, 3187917, 3277611, 3295821, 3767331, 4686039, 5059881
Offset: 1

Views

Author

M. F. Hasler, Aug 22 2009

Keywords

Comments

A subsequence of A011257.
If 3^{k+1}-1 = d*D such that p = 2*b^{k+1}*(d+1) - 1 and q = 2*(b^{k+1}+D)-1 are distinct primes, then n = 3^k*p*q is a term of this sequence.
The same theorem holds for sequences of numbers such that sigma/phi=b^2/(b-1)^2 with other primes b (here b=3; in A068390: b=2, in A164648: b=5).

Links

Crossrefs

Cf. A000010 (=phi), A000203 (=sigma), A068390 (sigma/phi=4), A163667 (sigma/phi=9), A164647 (sigma/phi=16/9).

Programs

  • Mathematica
    Select[Range[506*10^4],DivisorSigma[1,#]/EulerPhi[#]==9/4&] (* Harvey P. Dale, Jun 22 2019 *)
  • PARI
    for( n=1,1e7, sigma(n)==9/4*eulerphi(n) && print1(n","))

A164650 Numbers n such that sigma(n)/phi(n) = 49/36.

Original entry on oeis.org

679, 10127, 20273, 672203, 971261, 1133639, 1247129, 1336231, 1646743, 1701089, 2369471, 2674969, 2722499, 2989909, 3160079, 3597659, 4545749, 6333503, 7127861, 9357101, 10574629, 20070061, 52928293, 67931137, 74731807, 79940069, 80704813, 93444911, 128155333
Offset: 1

Views

Author

M. F. Hasler, Aug 22 2009

Keywords

Comments

A subsequence of A011257.
If 7^{k+1}-1 = d*D such that p = 2*7^{k+1}*(d+1)-1 and q = 2*(7^{k+1}+D)-1 are distinct primes, then n = 7^k*p*q is a term of this sequence.
The same theorem holds for sequences of numbers such that sigma/phi=b^2/(b-1)^2 with other primes b (here b=7), cf. A068390, A164646, A164648.

Links

Crossrefs

Cf. A000010 (=phi), A000203 (=sigma), A068390 (sigma/phi=4), A163667 (sigma/phi=9), A164646-A164649.

Programs

  • PARI
    for( n=1,1e7, sigma(n)==49/36*eulerphi(n) && print1(n","))

A165630 Numbers n such that sigma(n)/phi(n) = 25/9, where sigma = A000203, phi = A000010.

Original entry on oeis.org

8721, 10179, 21489, 99813, 203721, 228417, 229653, 250705, 268047, 609957, 1150713, 1343277, 2429283, 2835417, 2835807, 2881197, 3150333, 3230469, 3833181, 4679157, 4885569, 5673291, 6082527, 6302529, 6713637, 6819879, 7096329, 9464121, 10313979, 12168651
Offset: 1

Views

Author

Farideh Firoozbakht and M. F. Hasler, Sep 23 2009

Keywords

Comments

A subsequence of A011257. Contains the product m*n of relatively prime (gcd(m,n)=1) terms (m,n) in A164647 x A164648.

Links

Programs

  • Mathematica
    Select[Range[122*10^5],DivisorSigma[1,#]/EulerPhi[#]==25/9&] (* Harvey P. Dale, Jun 20 2021 *)
  • PARI
    for( i=1,1e7, sigma(i)/eulerphi(i)==25/9 && print1(i", "))

A165629 Numbers n such that sigma(n)/phi(n) = 25/4, where sigma = A000203, phi = A000010.

Original entry on oeis.org

760, 11020, 18088, 21112, 58206, 65262, 71630, 100280, 123424, 142688, 262276, 303212, 332710, 630344, 679070, 761390, 1265096, 1369120, 1454060, 1454260, 1462552, 1704794, 2185750, 2386664, 2627548, 2783872, 2786056, 2909380, 2927848, 5207680, 5289220
Offset: 1

Views

Author

Farideh Firoozbakht and M. F. Hasler, Sep 23 2009

Keywords

Comments

A subsequence of A011257. Contains the product m*n of relatively prime (gcd(m,n)=1) terms (m,n) in A068390 x A164648 and in A164646 x A165630.

Links

Programs

  • Mathematica
    Select[Range[5300000],4*DivisorSigma[1,#]==25*EulerPhi[#]&] (* Harvey P. Dale, May 09 2012 *)
  • PARI
    for( i=1,1e9, sigma(i)*4-25*eulerphi(i) || print1(i", "))
Showing 1-4 of 4 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.