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

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

Author

M. F. Hasler, Aug 22 2009

Keywords

• nonn
• changed

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

• 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), 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