The OEIS is supported by the many generous donors to the OEIS Foundation. Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 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 (list; graph; refs; listen; history; text; internal format)
 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 3-perfect (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, 1-2-3, Spring 2000. LINKS R. J. Mathar, Table of n, a(n) for n = 1..1000 Amarnath Murthy and Charles Ashbacher, Generalized Partitions and Some New Ideas on Number Theory and Smarandache Sequences, Hexis, Phoenix; USA 2005. See Section 1.4, 1.12. Eric Weisstein's World of Mathematics, Divisor Product FORMULA Union of A050997 and A054753. - Lekraj Beedassy, Jul 13 2005 A000005(a(n))=6. - Juri-Stepan Gerasimov, Oct 10 2009 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): sort(convert(S, list)); # Robert Israel, Feb 10 2016 MATHEMATICA f[n_]:=Length[Divisors[n]]==6; lst={}; Do[If[f[n], AppendTo[lst, n]], {n, 6!}]; lst (* Vladimir Joseph Stephan Orlovsky, Dec 14 2009 *) Select[Range, DivisorSigma[0, #]==6&] (* Harvey P. Dale, Oct 02 2014 *) PROG (PARI) is(n)=numdiv(n)==6 \\ Charles R Greathouse IV, Jan 23 2014 (Python) from sympy import divisor_count def ok(n): return divisor_count(n) == 6 print([k for k in range(429) if ok(k)]) # Michael S. Branicky, Dec 18 2021 CROSSREFS Cf. A061117. Sequence in context: A263838 A217856 A253388 * A162947 A351201 A359892 Adjacent sequences: A030512 A030513 A030514 * A030516 A030517 A030518 KEYWORD nonn,easy AUTHOR Jeff Burch EXTENSIONS Definition clarified by Jonathan Sondow, Jan 23 2014 STATUS approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recents
The OEIS Community | Maintained by The OEIS Foundation Inc.

Last modified October 2 17:28 EDT 2023. Contains 365837 sequences. (Running on oeis4.)