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 A002035 Numbers that contain primes to odd powers only. (Formerly M0614 N0224) 14
 2, 3, 5, 6, 7, 8, 10, 11, 13, 14, 15, 17, 19, 21, 22, 23, 24, 26, 27, 29, 30, 31, 32, 33, 34, 35, 37, 38, 39, 40, 41, 42, 43, 46, 47, 51, 53, 54, 55, 56, 57, 58, 59, 61, 62, 65, 66, 67, 69, 70, 71, 73, 74, 77, 78, 79, 82, 83, 85, 86, 87, 88, 89, 91, 93, 94, 95, 96, 97, 101 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS Complement of the union of {1} and A072587. - Reinhard Zumkeller, Nov 15 2012, corrected version from Jun 23 2002 A036537 is a subsequence and this sequence is a subsequence of A162644. - Reinhard Zumkeller, Jul 08 2009 Numbers whose sum of divisors is equal to the sum of bi-unitary divisors: A000203(a(n)) = A188999(a(n)). - Paolo P. Lava, Oct 08 2014 REFERENCES N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence). N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence). LINKS T. D. Noe, Table of n, a(n) for n = 1..1000 E. Cohen, Quadratic congruences with an odd number of summands, Amer. Math. Monthly, 73 (1966), 138-143. MAPLE isA002035 := proc(n)     local pe;     for pe in ifactors(n)[2] do         if type(pe[2], 'even') then             return false;         end if;     end do:     true ; end proc: A002035 := proc(n)     option remember;     if n =1 then         2;     else         for a from procname(n-1)+1 do             if isA002035(a) then                 return a;             end if;         end do:     end if; end proc: seq(A002035(n), n=1..100) ; # R. J. Mathar, Nov 27 2017 MATHEMATICA ok[n_] := And @@ OddQ /@ FactorInteger[n][[All, 2]]; Select[Range[2, 101], ok] (* Jean-François Alcover, Apr 22 2011 *) PROG (Haskell) a002035 n = a002035_list !! (n-1) a002035_list = filter (all odd . a124010_row) [1..] -- Reinhard Zumkeller, Nov 14 2012 (PARI) is(n)=Set(factor(n)[, 2]%2)==[1] \\ Charles R Greathouse IV, Feb 07 2017 CROSSREFS Cf. A072586, A124010, A295316. Sequence in context: A239161 A162644 A268335 * A036537 A072510 A084116 Adjacent sequences:  A002032 A002033 A002034 * A002036 A002037 A002038 KEYWORD nonn,nice AUTHOR EXTENSIONS More terms from Reinhard Zumkeller, Jun 23 2002 STATUS approved

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Last modified October 17 12:21 EDT 2019. Contains 328111 sequences. (Running on oeis4.)