A247079 - OEIS

%I #33 Dec 10 2016 19:36:23

%S 345,1050,1645,4386,6489,8041,13026,23881,88473,115957,255041,342637,

%T 377201,1497517,2132021,2428489,3256261,3847001,4114285,4646101,

%U 5054221,6816865,7218641,7587901,13384681,14872837,17897737,20901553,23807821,25863653,28207957

%N Numbers for which the harmonic mean of nontrivial divisors is an integer and which are not a square of prime numbers.

%C That's the numbers which are in A247078 and not in A001248.

%C a(149) >= 2*10^11. - _Hiroaki Yamanouchi_, Nov 20 2014

%H Daniel Lignon and Hiroaki Yamanouchi, <a href="/A247079/b247079.txt">Table of n, a(n) for n = 1..148</a> (terms a(1)-a(40) from Daniel Lignon)

%e 345 is not the square of a prime number and the nontrivial divisors of 345 are [3,5,15,23,69,115]. Their harmonic mean is 6/(1/3+1/5+1/15+1/23+1/69+1/115)=9.

%o (PARI) isok(n) = !(issquare(n) && isprime(sqrtint(n))) && (d=divisors(n)) && (#d > 2) && (denominator((#d-2)/sum(i=2, #d-1, 1/d[i])) == 1); \\ _Michel Marcus_, Nov 17 2014

%Y Cf. A001599 (harmonic numbers), A247078.

%K nonn

%O 1,1

%A _Daniel Lignon_, Nov 17 2014

%E a(15)-a(24) from _Michel Marcus_, Nov 17 2014