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 A082294 Numbers having exactly two square divisors > 1. 5
 16, 32, 48, 80, 81, 96, 112, 160, 162, 176, 208, 224, 240, 243, 272, 304, 336, 352, 368, 405, 416, 464, 480, 486, 496, 528, 544, 560, 567, 592, 608, 624, 625, 656, 672, 688, 736, 752, 810, 816, 848, 880, 891, 912, 928, 944, 976, 992, 1040, 1053, 1056, 1072 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS Numbers of the form p^e * s where p is prime, e is 4 or 5 and s is squarefree and coprime to p. - David A. Corneth, Sep 01 2020 The asymptotic density of this sequence is (6/Pi^2) * Sum_{p prime} (1/(p^3*(p+1)) + 1/(p^4*(p+1))) = 0.04680621631952059947... . - Amiram Eldar, Sep 25 2022 LINKS David A. Corneth, Table of n, a(n) for n = 1..10000 FORMULA A046951(a(n)) = 3. EXAMPLE 81 has 3 square divisors: 1, 9 and 81, therefore 81 is a term. MATHEMATICA Select[Range[1000], MemberQ[{{4}, {5}}, Select[FactorInteger[#][[;; , 2]], #1 > 1 &]] &] (* Amiram Eldar, Sep 01 2020 *) PROG (PARI) is(n)=my(f=vecsort(factor(n)[, 2], , 4)); if(#f==1, f[1]>3&&f[1]<6, #f>1 && f[1]>3 && f[1]<6 && f[2]==1) \\ Charles R Greathouse IV, Oct 16 2015 CROSSREFS Cf. A082295, A046951, A048111, A013929. Sequence in context: A043334 A023707 A044442 * A048946 A260050 A224544 Adjacent sequences: A082291 A082292 A082293 * A082295 A082296 A082297 KEYWORD nonn AUTHOR Reinhard Zumkeller, Apr 08 2003 STATUS approved

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Last modified September 7 16:30 EDT 2024. Contains 375749 sequences. (Running on oeis4.)