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A212167
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Numbers n such that the maximal exponent in its prime factorization is not greater than the number of positive exponents (A051903(n) <= A001221(n)).
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10
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1, 2, 3, 5, 6, 7, 10, 11, 12, 13, 14, 15, 17, 18, 19, 20, 21, 22, 23, 26, 28, 29, 30, 31, 33, 34, 35, 36, 37, 38, 39, 41, 42, 43, 44, 45, 46, 47, 50, 51, 52, 53, 55, 57, 58, 59, 60, 61, 62, 63, 65, 66, 67, 68, 69, 70, 71, 73, 74, 75, 76, 77, 78, 79, 82, 83
(list;
graph;
refs;
listen;
history;
text;
internal format)
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OFFSET
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1,2
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COMMENTS
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REFERENCES
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M. Abramowitz and I. A. Stegun, eds., Handbook of Mathematical Functions, National Bureau of Standards Applied Math. Series 55, 1964 (and various reprintings), p. 844.
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LINKS
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M. Abramowitz and I. A. Stegun, eds., Handbook of Mathematical Functions, National Bureau of Standards, Applied Math. Series 55, Tenth Printing, 1972 [alternative scanned copy].
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EXAMPLE
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40 = 2^3*5^1 has 2 distinct prime factors, hence, 2 positive exponents in its prime factorization (although the 1 is often left implicit). 2 is less than the maximal exponent in 40's prime factorization, which is 3. Therefore, 40 does not belong to the sequence. But 10 = 2^1*5^1 and 20 = 2^2*5^1 belong, since the maximal exponents in their prime factorizations are 1 and 2 respectively.
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MAPLE
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isA212167 := proc(n)
end proc:
for n from 1 to 1000 do
if isA212167(n) then
printf("%d, ", n) ;
end if;
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MATHEMATICA
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okQ[n_] := Module[{f = Transpose[FactorInteger[n]][[2]]}, Max[f] <= Length[f]]; Select[Range[1000], okQ] (* T. D. Noe, May 24 2012 *)
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PROG
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(Haskell)
import Data.List (findIndices)
a212167 n = a212167_list !! (n-1)
a212167_list = map (+ 1) $ findIndices (>= 0) a225230_list
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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