A364433 Numbers with multiplicities of primes per mod 3 residue in nonincreasing order.
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
Offset: 1
Keywords
Examples
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.
Programs
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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)))
Comments