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 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 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 COMMENTS Terms of A364583 are in this sequence. LINKS Table of n, a(n) for n=1..60. 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 Cf. A000244, A025487, A364583. Sequence in context: A358330 A093686 A325031 * A155763 A347350 A030319 Adjacent sequences: A364430 A364431 A364432 * A364434 A364435 A364436 KEYWORD nonn AUTHOR David A. Corneth, Aug 06 2023 STATUS approved

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Last modified August 11 04:26 EDT 2024. Contains 375059 sequences. (Running on oeis4.)