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A324212 Numbers k such that the sum of the binary digits of the exponents of the prime factorization of k is even and k is a product of primorials. 1
1, 6, 8, 12, 32, 36, 48, 64, 120, 144, 210, 216, 360, 384, 420, 480, 512, 768, 864, 960, 1024, 1152, 1260, 1296, 1440, 1680, 1728, 1800, 2160, 2304, 2880, 4096, 5040, 6144, 6300, 7200, 7560, 7680, 7776, 9240, 10368, 10800, 12960, 13440, 13824, 14400, 15360, 15552, 17280 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

This sequence is a primitive subsequence of A000379; it lists minimal terms in that sequence having their prime exponents.

LINKS

David A. Corneth, Table of n, a(n) for n = 1..10000

EXAMPLE

360 is a term as 360 = 2^3 * 3^2 * 5 which has exponents in binary 11_2, 10_2 and 1_2 respectively. The sum of binary digits of those exponents is (1 + 1) + (1 + 0) + 1 = 4 which is even. Furthermore, 360 is a product of primorials; 360 = 30 * 6 * 2. Therefore, 360 is in the sequence.

PROG

is(n) = {if(n==1, return(1)); 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 A000379 and A025487.

Sequence in context: A212351 A327240 A274001 * A160133 A057710 A285678

Adjacent sequences:  A324209 A324210 A324211 * A324213 A324214 A324215

KEYWORD

nonn

AUTHOR

David A. Corneth, Mar 20 2019

STATUS

approved

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Last modified February 24 16:41 EST 2020. Contains 332209 sequences. (Running on oeis4.)