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A002734
Remove squares!
(Formerly M0611 N0222)
3
2, 3, 5, 6, 7, 2, 10, 11, 3, 13, 14, 15, 17, 2, 19, 5, 21, 22, 23, 6, 26, 3, 7, 29, 30, 31, 2, 33, 34, 35, 37, 38, 39, 10, 41, 42, 43, 11, 5, 46, 47, 3, 2, 51, 13, 53, 6, 55, 14, 57, 58, 59, 15, 61, 62, 7, 65, 66, 67, 17, 69, 70, 71, 2, 73, 74, 3, 19, 77, 78, 79
OFFSET
1,1
COMMENTS
This is a riddle. (Explanation: This lists the squarefree part of the nonsquares. - Amiram Eldar, Sep 05 2020)
A007913 with the ones removed.
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
H. Brocard, Notes élémentaires sur le problème de Peel, Nouvelle Correspondance Mathématique, Vol. 4 (1878), pp. 161-169.
FORMULA
a(n) = A007913(A000037(n)). - Amiram Eldar, Sep 05 2020
Sum_{k=1..n} a(k) ~ c * n^2, where c = Pi^2/30 = 0.328986... . - Amiram Eldar, Feb 02 2024
MATHEMATICA
core[n_] := Times @@ (First[#]^Mod[Last[#], 2] & /@ FactorInteger[n]); Select[core /@ Range[100], # > 1 &] (* Amiram Eldar, Sep 05 2020 *)
CROSSREFS
Intersection of A000037 and A007913.
Sequence in context: A175081 A023834 A084735 * A367417 A339949 A160100
KEYWORD
nonn
STATUS
approved