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%I #17 Jan 25 2024 15:06:15
%S 2,4,16,24,30,60,72,96,128,180,192,240,256,288,432,576,720,840,900,
%T 1080,1536,1920,2048,2310,2520,2592,3072,3360,3456,3600,3840,4320,
%U 4608,4620,5184,5400,5760,6480,6720,6912,8192,8640,9216,10080,11520,12288,12600,13860,15120
%N Numbers k such that the sum of the binary digits of the exponents of the prime factorization of k is odd and k is a product of primorials.
%C This sequence is a primitive sequence of A000028; it lists minimal terms in that sequence having their prime exponents.
%e 180 is a term as 180 = 2^2 * 3^2 * 5 which has exponents in binary 10_2, 10_2 and 1_2 respectively. The sum of binary digits of those exponents is (1 + 0) + (1 + 0) + 1 = 3 which is odd. Furthermore, 180 is a product of primorials; 180 = 30 * 6. Therefore, 180 is in the sequence.
%o (PARI) is(n) = {if(n==1, return(0)); my(f = factor(n)); f[#f~, 1] == prime(#f~) && vecsort(f[, 2],,4) == f[, 2] && sum(i=1, #f~, hammingweight(f[i, 2]))%2}
%Y Intersection of A000028 and A025487.
%K nonn,base
%O 1,1
%A _David A. Corneth_, Mar 20 2019
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