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

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

Author

M. F. Hasler, Aug 22 2009

Keywords

• nonn

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

• Donovan Johnson, Table of n, a(n) for n = 1..1000

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","))