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 A002734 Remove squares! (Formerly M0611 N0222) 3

%I M0611 N0222 #25 Feb 02 2024 11:02:14

%S 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,

%T 33,34,35,37,38,39,10,41,42,43,11,5,46,47,3,2,51,13,53,6,55,14,57,58,

%U 59,15,61,62,7,65,66,67,17,69,70,71,2,73,74,3,19,77,78,79

%N Remove squares!

%C This is a riddle. (Explanation: This lists the squarefree part of the nonsquares. - _Amiram Eldar_, Sep 05 2020)

%C A007913 with the ones removed.

%D N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).

%D N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

%H Amiram Eldar, <a href="/A002734/b002734.txt">Table of n, a(n) for n = 1..10000</a>

%H H. Brocard, <a href="https://gdz.sub.uni-goettingen.de/id/PPN598948236_0004?tify={%22pages%22:[187],%22view%22:%22info%22}">Notes élémentaires sur le problème de Peel</a>, Nouvelle Correspondance Mathématique, Vol. 4 (1878), pp. 161-169.

%F a(n) = A007913(A000037(n)). - _Amiram Eldar_, Sep 05 2020

%F Sum_{k=1..n} a(k) ~ c * n^2, where c = Pi^2/30 = 0.328986... . - _Amiram Eldar_, Feb 02 2024

%t core[n_] := Times @@ (First[#]^Mod[Last[#], 2] & /@ FactorInteger[n]); Select[core /@ Range[100], # > 1 &] (* _Amiram Eldar_, Sep 05 2020 *)

%Y Intersection of A000037 and A007913.

%K nonn

%O 1,1

%A _N. J. A. Sloane_

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Last modified September 11 17:54 EDT 2024. Contains 375839 sequences. (Running on oeis4.)