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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. 0
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 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

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

LINKS

Table of n, a(n) for n=1..49.

EXAMPLE

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.

PROG

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}

CROSSREFS

Intersection of A000028 and A025487.

Sequence in context: A253143 A193868 A256788 * A059622 A131475 A239363

Adjacent sequences:  A324208 A324209 A324210 * A324212 A324213 A324214

KEYWORD

nonn,base

AUTHOR

David A. Corneth, Mar 20 2019

STATUS

approved

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Last modified September 27 17:05 EDT 2021. Contains 347693 sequences. (Running on oeis4.)