

A030515


Numbers with exactly 6 divisors.


16



12, 18, 20, 28, 32, 44, 45, 50, 52, 63, 68, 75, 76, 92, 98, 99, 116, 117, 124, 147, 148, 153, 164, 171, 172, 175, 188, 207, 212, 236, 242, 243, 244, 245, 261, 268, 275, 279, 284, 292, 316, 325, 332, 333, 338, 356, 363, 369, 387, 388, 404, 412, 423, 425, 428
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OFFSET

1,1


COMMENTS

Numbers which are either the 5th power of a prime or the product of a prime and the square of a different prime, i.e., numbers which are in A050997 (5th powers of primes) or A054753.  Henry Bottomley, Apr 25 2000
Also numbers which are the square root of the product of their proper divisors.  Amarnath Murthy, Apr 21 2001
Such numbers are multiplicatively 3perfect (i.e., the product of divisors of a(n) equals a(n)^3).  Lekraj Beedassy, Jul 13 2005
Since A119479(6)=5, there are never more than 5 consecutive terms. Quintuples of consecutive terms start at 10093613546512321, 14414905793929921, 266667848769941521, ... (A141621). No such quintuple contains a term of the form p^5.  Ivan Neretin, Feb 08 2016


REFERENCES

Amarnath Murthy, A note on the Smarandache Divisor sequences, Smarandache Notions Journal, Vol. 11, 123, Spring 2000.


LINKS



FORMULA



MAPLE

N:= 1000: # to get all terms <= N
Primes:= select(isprime, {2, seq(i, i=3..floor(N/4))}):
S:= select(`<=`, {seq(p^5, p = Primes), seq(seq(p*q^2, p=Primes minus {q}), q=Primes)}, N):


MATHEMATICA

Select[Range[500], DivisorSigma[0, #]==6&] (* Harvey P. Dale, Oct 02 2014 *)


PROG

(Python)
from sympy import divisor_count
def ok(n): return divisor_count(n) == 6


CROSSREFS



KEYWORD

nonn,easy


AUTHOR



EXTENSIONS



STATUS

approved



