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, 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

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

(PARI) 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: A361968 A327240 A274001 * A160133 A057710 A285678

Adjacent sequences: A324209 A324210 A324211 * A324213 A324214 A324215

Keyword

nonn

Author

David A. Corneth, Mar 20 2019

Status

approved