A324211 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.

2, 4, 16, 24, 30, 60, 72, 96, 128, 180, 192, 240, 256, 288, 432, 576, 720, 840, 900, 1080, 1536, 1920, 2048, 2310, 2520, 2592, 3072, 3360, 3456, 3600, 3840, 4320, 4608, 4620, 5184, 5400, 5760, 6480, 6720, 6912, 8192, 8640, 9216, 10080, 11520, 12288, 12600, 13860, 15120

Offset: 1

Author

David A. Corneth, Mar 20 2019

Keywords

• nonn
• base

Comments

This sequence is a primitive sequence of A000028; it lists minimal terms in that sequence having their prime exponents.

Examples

			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.
		

Crossrefs

Intersection of A000028 and A025487.

Programs

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}