OFFSET
1,2
COMMENTS
EXAMPLE
1/2 + 1/3 - 1/6 = 2/3,
1/3 + 1/5 + 1/7 - 1/105 = 2/3,
1/2 + 1/5 + 1/7 + 1/19 - 1/1330 = 17/19,
....
6 = 2*3, 105 = 3*5*7, 1330 = 2*5*7*19, 331230 = 2*3*5*61*181, 127357230 = 2*3*5*17*53*151, ... - Jonathan Sondow, Jul 27 2019
MATHEMATICA
m=2; s={}; Do[f = FactorInteger[n]; p = f[[;; , 1]]; e = f[[;; , 2]]; If[Max[e] > 1 || Length[e] < m, Continue[]]; frac = Total@(1/p) - 1/n; num = Numerator[frac]; den = Denominator[frac]; If[den != num && PrimeQ[num] && PrimeQ[den], AppendTo[s, n]; m++], {n, 1, 5*10^6}]; s
PROG
(PARI) a(n) = {for(i = 2, oo, if(is(i, n), return(i)))}
is(m, qp) = {my(f = factor(m)); if(#f~ != qp, return(0)); if(Set(f[, 2]) != Set([1]), return(0)); s = sum(i = 1, qp, 1/f[i, 1]) - 1/m; isprime(denominator(s)) && isprime(numerator(s))} \\ David A. Corneth, Jul 27 2019
CROSSREFS
KEYWORD
nonn,hard
AUTHOR
Amiram Eldar and Thomas Ordowski, Jul 26 2019
STATUS
approved