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

1,2

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