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 A065036 Product of the cube of a prime (A030078) and a different prime. 37
 24, 40, 54, 56, 88, 104, 135, 136, 152, 184, 189, 232, 248, 250, 296, 297, 328, 344, 351, 375, 376, 424, 459, 472, 488, 513, 536, 568, 584, 621, 632, 664, 686, 712, 776, 783, 808, 824, 837, 856, 872, 875, 904, 999, 1016, 1029, 1048, 1096, 1107, 1112 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS This sequence appears on row 8 of the list illustrated in A064839 and is similar to A054753 which appears on row 6. Previous rows are generated by A000007, A000040, A001248, A006881, A030078 respectively. Or, the numbers n such that 20=number of perfect partitions of n. - Juri-Stepan Gerasimov, Sep 26 2009 A089233(a(n)) = 3. - Reinhard Zumkeller, Sep 04 2013 LINKS T. D. Noe, Table of n, a(n) for n = 1..1000 FORMULA A002033(a(n)) = 20. - Juri-Stepan Gerasimov, Sep 26 2009 Solutions of the equation tau(n^3)=5*tau(n). - Paolo P. Lava, Mar 15 2013 A000005(a(n)) = 8. - Altug Alkan, Nov 11 2015 EXAMPLE a(4)= 56 since 56 = 2*2*2*7. MAPLE with(numtheory); A065036:=proc(q) local n; for n from 1 to q do if tau(n^3)=5*tau(n) then print(n); fi; od; end: A065036(10^10); # Paolo P. Lava, Mar 15 2013 MATHEMATICA Select[ Range[1500], Sort[ Transpose[ FactorInteger[ # ]] [[2]]] == {1, 3} & ] Module[{upto=1200}, Select[(Union[Flatten[{#[[1]]^3 #[[2]], #[[1]]#[[2]]^3}&/@Subsets[Prime[Range[upto/8]], {2}]]]), #<=upto&]] (* Harvey P. Dale, May 23 2015 *) PROG (PARI) list(lim)=my(v=List(), t); forprime(p=2, (lim\2)^(1/3), t=p^3; forprime(q=2, lim\t, if(p==q, next); listput(v, t*q))); vecsort(Vec(v)) \\ Charles R Greathouse IV, Jul 20 2011 (PARI) is(n)=my(f=factor(n)[, 2]); f==[3, 1]~||f==[1, 3]~ \\ Charles R Greathouse IV, Oct 15 2015 CROSSREFS Cf. A000007, A000040, A001248, A002033, A006881, A030078, A054753, A064839. Sequence in context: A334801 A297401 A065127 * A329880 A303359 A340747 Adjacent sequences: A065033 A065034 A065035 * A065037 A065038 A065039 KEYWORD easy,nonn AUTHOR Alford Arnold, Nov 04 2001 STATUS approved

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Last modified December 7 22:02 EST 2022. Contains 358671 sequences. (Running on oeis4.)