A066110 - OEIS

A066110

Primes of form sigma_4(n)/sigma_2(n), arising in A066109.

13, 73, 313, 601, 28393, 83233, 922561, 3416953, 13842121, 47451433, 141146281, 212601841, 234750601, 294482761, 2750006041, 3262751521, 4362404353, 4784281393, 5236041961, 9354855121, 9597826993, 13564461457, 16936647121

(list; graph; refs; listen; history; text; internal format)

OFFSET

1,1

LINKS

Harry J. Smith, Table of n, a(n) for n=1..250

FORMULA

Primes of form A001159(A066109(n))/A001157(A066109(n)).

EXAMPLE

m=20: divisors(20) = {20,10,5,4,2,1}, sigma_4 = 160000 + 10000 + 625 + 256 + 16 + 1 = 170898, sigma_2 = 400 + 100 + 25 + 16 + 4 + 1 = 546; p = 170898/546 = 73 is prime, the 2nd term.

MATHEMATICA

Do[s=DivisorSigma[4, n]; z=DivisorSigma[2, n]; If[PrimeQ[s/z], Print[{n, s, z, s/z}]], {n, 1, 10000000}] Output=s/z.

Select[Table[DivisorSigma[4, n]/DivisorSigma[2, n], {n, 200000}], PrimeQ] (* Harvey P. Dale, Jan 31 2022 *)

PROG

(PARI) { n=0; for (m=1, 10^9, if (frac(f=sigma(m, 4)/sigma(m, 2)), next); if (isprime(f), write("b066110.txt", n++, " ", f); if (n==250, return)) ) } \\ Harry J. Smith, Feb 01 2010

CROSSREFS

Cf. A000040, A001157, A001159, A066109-A066113.

Sequence in context: A143008 A107963 A006230 * A020527 A146618 A220414

Adjacent sequences: A066107 A066108 A066109 * A066111 A066112 A066113

KEYWORD

nonn

AUTHOR

Labos Elemer, Dec 05 2001

STATUS

approved