A364433 - OEIS

%I #9 Aug 24 2023 10:22:08

%S 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,

%T 54,56,60,63,64,70,72,80,81,84,90,91,96,98,100,108,110,112,120,126,

%U 128,140,144,147,160,162,168,180,182,189,192,196,200,210,216

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

%C Terms of A364583 are in this sequence.

%e 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.

%o (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)))

%Y Cf. A000244, A025487, A364583.

%K nonn

%O 1,2

%A _David A. Corneth_, Aug 06 2023