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 1-5 of 5 results.

A164648 Numbers k such that sigma(k)/phi(k) = 25/16.

Original entry on oeis.org

40859, 48505, 54385, 121771, 156125, 565607, 1154419, 1219933, 1294363, 2448397, 3590461, 9710975, 16067363, 16069573, 17984515, 19013455, 21341755, 25804115, 26515223, 27656155, 29655415, 30372605, 32101255, 34467653, 36546355, 38043943, 38645981, 39559219
Offset: 1

Views

Author

M. F. Hasler, Aug 22 2009

Keywords

Comments

A subsequence of A011257.
If 5^{k+1}-1 = d*D such that p = 2*5^{k+1}*(d+1)-1 and q = 2*(5^{k+1}+D)-1 are distinct primes, then n = 5^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=5), cf. A164646.

Links

Crossrefs

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

Programs

  • Mathematica
    Select[Range[2000000], DivisorSigma[1, #]/EulerPhi[#] == 25/16 &] (* Carl Najafi, Aug 16 2011 *)
  • PARI
    for( n=1,1e7, sigma(n)==25/16*eulerphi(n) && print1(n","))

Extensions

More terms from Carl Najafi, Aug 16 2011

A164647 Numbers n such that sigma(n)/phi(n) = 16/9.

Original entry on oeis.org

1463, 2945, 8255, 70091, 81809, 89999, 122759, 187625, 193039, 196469, 388585, 494665, 671365, 2311673, 2442583, 2687113, 4209985, 4705285, 4902247, 5393017, 5667389, 5866003, 9248323, 10795967, 11345411, 11670275, 11773027, 13290485, 13741273, 15978487
Offset: 1

Views

Author

M. F. Hasler, Aug 22 2009

Keywords

Comments

A subsequence of A011257.

Links

Crossrefs

Cf. A000010 (=phi), A000203 (=sigma), A068390, A163667, A164646.

Programs

  • PARI
    for( n=1,10^7, sigma(n)==16/9*eulerphi(n) && print1(n","))

Extensions

More terms from Farideh Firoozbakht, Sep 22 2009

A164649 Numbers n such that sigma(n)/phi(n) = 36/25.

Original entry on oeis.org

5797, 10153, 20377, 50953, 383719, 405449, 446039, 486421, 608399, 973709, 1321529, 1521311, 3086369, 3228511, 3451877, 3529813, 3859513, 4552373, 4767721, 5827679, 6194321, 6479599, 6724039, 6927893, 7038241, 7919197, 11696111, 15893773, 16894141, 16924873
Offset: 1

Views

Author

M. F. Hasler, Aug 22 2009

Keywords

Comments

A subsequence of A011257. See A164646-A164650 for related sequences.

Links

Crossrefs

Cf. A000010 (=phi), A000203 (=sigma), A068390 (sigma/phi=4), A163667 (sigma/phi=9), A164646-A164650.

Programs

  • PARI
    for( n=1,1e7, sigma(n)==36/25*eulerphi(n) && print1(n","))

Extensions

More terms from Sean A. Irvine, May 17 2010

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","))

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 1-5 of 5 results.

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