A247079 Numbers for which the harmonic mean of nontrivial divisors is an integer and which are not a square of prime numbers.

345, 1050, 1645, 4386, 6489, 8041, 13026, 23881, 88473, 115957, 255041, 342637, 377201, 1497517, 2132021, 2428489, 3256261, 3847001, 4114285, 4646101, 5054221, 6816865, 7218641, 7587901, 13384681, 14872837, 17897737, 20901553, 23807821, 25863653, 28207957

Offset

1,1

Comments

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

a(149) >= 2*10^11. - Hiroaki Yamanouchi, Nov 20 2014

Links

Daniel Lignon and Hiroaki Yamanouchi, Table of n, a(n) for n = 1..148 (terms a(1)-a(40) from Daniel Lignon)

Example

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.

Prog

(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

Crossrefs

Cf. A001599 (harmonic numbers), A247078.

Sequence in context: A116347 A063370 A095963 * A333079 A236731 A138043

Adjacent sequences: A247076 A247077 A247078 * A247080 A247081 A247082

Keyword

nonn

Author

Daniel Lignon, Nov 17 2014

Extensions

a(15)-a(24) from Michel Marcus, Nov 17 2014

Status

approved