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A225837 Numbers of form 2^i*3^j*(6k+1), i, j, k >= 0. 6
1, 2, 3, 4, 6, 7, 8, 9, 12, 13, 14, 16, 18, 19, 21, 24, 25, 26, 27, 28, 31, 32, 36, 37, 38, 39, 42, 43, 48, 49, 50, 52, 54, 55, 56, 57, 61, 62, 63, 64, 67, 72, 73, 74, 75, 76, 78, 79, 81, 84, 85, 86, 91, 93, 96, 97, 98, 100, 103, 104, 108, 109, 110, 111, 112 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,2
COMMENTS
The asymptotic density of this sequence is 1/2. - Amiram Eldar, Apr 03 2022
From Peter Munn, Nov 16 2023: (Start)
Contains all nonzero squares.
Dividing by 5 the terms that are multiples of 5 gives its complement, A225838.
(A352272, 2*A352272, 3*A352272, 6*A352272) is a partition of the terms.
The terms form a subgroup of the positive integers under the operation A059897(.,.) and are the positive integers in an index 2 multiplicative subgroup of rationals that is generated by 2, 3 and integers congruent to 1 modulo 6. See A225857 and A352272 for further information about such subgroups.
(End)
LINKS
MATHEMATICA
mx = 122; t = {}; Do[n = 2^i*3^j (6 k + 1); If[n <= mx, AppendTo[t, n]], {i, 0, Log[2, mx]}, {j, 0, Log[3, mx]}, {k, 0, mx/6}]; Union[t] (* T. D. Noe, May 16 2013 *)
PROG
(PARI) for(n=1, 200, t=n/(2^valuation(n, 2)*3^valuation(n, 3)); if((t%6==1), print1(n, ", ")))
(Magma) [n: n in [1..200] | IsOne(d mod 6) where d is n div (2^Valuation(n, 2)*3^Valuation(n, 3))]; // Bruno Berselli, May 16 2013
CROSSREFS
Complement of A225838.
Subsequences: A003136\{0}, A083854\{0}, A260488\{0}, A352272.
Symmetric difference of A026225 and A036554; of A036668 and A189716.
Sequence in context: A285986 A101883 A236207 * A035246 A356955 A112258
KEYWORD
nonn,easy
AUTHOR
Ralf Stephan, May 16 2013
STATUS
approved

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Last modified March 28 05:02 EDT 2024. Contains 371235 sequences. (Running on oeis4.)