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Numbers that are either an odd squarefree number squared or twice such a number.
1

%I #14 Jan 11 2023 14:49:45

%S 1,2,9,18,25,49,50,98,121,169,225,242,289,338,361,441,450,529,578,722,

%T 841,882,961,1058,1089,1225,1369,1521,1681,1682,1849,1922,2178,2209,

%U 2450,2601,2738,2809,3025,3042,3249,3362,3481,3698,3721,4225,4418,4489,4761,5041,5202,5329,5618,5929,6050,6241

%N Numbers that are either an odd squarefree number squared or twice such a number.

%C Numbers in whose prime factorization the exponent of 2 can be only 0 or 1, and the exponent of any odd prime can be only 0 or 2.

%F Sum_{n>=1} 1/a(n) = 18/Pi^2. - _Amiram Eldar_, Jan 07 2023

%t Select[Range[6000], (e = IntegerExponent[#, 2]) < 2 && SquareFreeQ[Sqrt[#/2^e]] &] (* _Amiram Eldar_, Jan 07 2023 *)

%o (PARI) isA359580(n) = A359549(n);

%o (Python)

%o from itertools import count, islice

%o from sympy import factorint

%o def A359580_gen(startvalue=1): # generator of terms >= startvalue

%o return filter(lambda n:(m:=(~n & n-1).bit_length())<=1 and all(e==2 for e in factorint(n>>m).values()),count(max(startvalue,1)))

%o A359580_list = list(islice(A359580_gen(),20)) # _Chai Wah Wu_, Jan 11 2023

%Y Cf. A359549 (characteristic function).

%Y Positions of odd terms in A046692, A327276, A327278, A359548.

%Y Cf. also A056911, A062503.

%K nonn

%O 1,2

%A _Antti Karttunen_, Jan 07 2023