A190880 a(n) is the smallest number k having n prime distinct divisors such that k is divisible by the square of the sum of its prime divisors.

300, 37026, 81900, 3719430, 60960900, 746876130, 37456118700, 1371798057630, 45093761813100, 1750692518344770, 72411562719475980, 4075432279946977950, 430815330651894087900

Offset

3,1

Comments

n > = 3, because if n = 2 then k = p^a * q^b, where p and q are distinct primes and (p+q)^2 | k => p+q ==0 (mod p) or 0 (mod (q), but p==0 (mod q) and q==0 (mod p) are impossible.

Links

Table of n, a(n) for n=3..15.

Charles R Greathouse IV, GP script for computing terms

Example

a(4) = 37026 because the prime distinct divisors of this number are {2, 3, 11, 17}, (2 + 3 + 11 + 17)^2 = 1089, and 37026 = 1089*34.

Maple

with(numtheory):for n from 3 to 10 do:id:=0:for k from 1 to 5000000 while(id=0)
  do:x:=factorset(k):n1:=nops(x):s:=0:for p from 1 to n1 do: s:=s+x[p]:od:s:=s^2:if
  n1= n and irem(k, s)=0 then id:=1:printf ( "%d %d \n", n, k):else fi:od:od:

Prog

(PARI) \\ See links for script.

Crossrefs

Cf. A190879.

Sequence in context: A241943 A036517 A223350 * A063935 A294687 A015275

Adjacent sequences: A190877 A190878 A190879 * A190881 A190882 A190883

Keyword

nonn,hard

Author

Michel Lagneau, May 23 2011

Extensions

a(8)-a(13) from Charles R Greathouse IV, May 23 2011

a(14)-a(15) from Charles R Greathouse IV, May 24 2011

Status

approved