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A177078
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Central polygonal-free numbers.
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0
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3, 5, 9, 13, 15, 17, 19, 23, 25, 27, 31, 39, 41, 43, 45, 47, 51, 53, 57, 59, 61, 65, 69, 71, 73, 75, 81, 83, 85, 89, 93, 95, 97, 101, 103, 107, 109, 113, 115, 117, 123, 125, 127, 129, 131, 135, 139, 141, 149, 151, 153, 155, 157, 159, 163, 167, 169, 171, 173, 177, 179
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OFFSET
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1,1
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COMMENTS
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Positive integers not multiples of any element except 1 of A000124. Complement of multiples of central polygonal numbers (other than multiples of 1, which are all integers) = {2, 4, 6, 7, 8, 10, 12, 14, 16, 18, 20, 21, 22, 24, ...}. This is to squarefree numbers (A005117), i.e., numbers that are not divisible by a square greater than 1, as central polygonal numbers (A000124) are to squares (A000290).
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LINKS
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FORMULA
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{a(n)} = {k such that k>0 and for no j>1 does A000124(j) | k} = {k such that k>0 and for no j>1 does (j(j+1)/2 + 1) | k}.
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EXAMPLE
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Construct by sieve. Start with all integers from 2 through N. Eliminate all multiples of A000124(1) = 2. Now we have all odd numbers. It is redundant to eliminate all multiples of A000124(2) = 4 as those were all eliminated in the previous step. Now eliminate all multiples of A000124(3) = 7. Now eliminate all multiples of A000124(4) = 11. Continue through eliminating all multiples of A000124 elements > 1 through N and one has all elements of this new sequence through N^2.
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MAPLE
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A000124 := proc(n) n*(n+1)/2+1 ; end proc:
isA177078 := proc(n) for j from 1 do if n mod A000124(j) = 0 then return false; elif A000124(j)> n then return true; end if; end do: end proc:
for n from 2 to 300 do if isA177078(n) then printf("%d, ", n) ; end if; end do: # R. J. Mathar, May 28 2010
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CROSSREFS
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KEYWORD
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easy,nonn
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AUTHOR
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EXTENSIONS
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9 inserted, 29 removed, 37 removed and sequence extended by R. J. Mathar, May 28 2010
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STATUS
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approved
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