

A364433


Numbers with multiplicities of primes per mod 3 residue in nonincreasing order.


0



1, 2, 3, 4, 6, 7, 8, 9, 10, 12, 14, 16, 18, 20, 21, 24, 27, 28, 30, 32, 36, 40, 42, 48, 49, 54, 56, 60, 63, 64, 70, 72, 80, 81, 84, 90, 91, 96, 98, 100, 108, 110, 112, 120, 126, 128, 140, 144, 147, 160, 162, 168, 180, 182, 189, 192, 196, 200, 210, 216
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OFFSET

1,2


COMMENTS

Terms of A364583 are in this sequence.


LINKS



EXAMPLE

60 = 2^2 * 3 * 5 is in the sequence as the prime factors with residue 2 (mod 3) are 2 and 5 and they have multiplicities 2 and 1 respectively. Those multiplicities are nonincreasing. Primes with residue 0 (mod 3) are 3 which have multiplicity 1. There are no prime factors with residue 1 (mod 3). So the multiplicities of all prime factors are nonincreasing for each residue mod 3.


PROG

(PARI) is(n) = my(es=vector(3, i, oo)); forprime(p=2, oo, v = valuation(n, p); if(es[p%3+1]>=v, es[p%3+1]=v, return(0)); n/=p^v; if(n==1, return(1)))


CROSSREFS



KEYWORD

nonn


AUTHOR



STATUS

approved



