A364583 -id:A364583 - cp's OEIS frontend

A364582 a(n) is the least number with exactly n divisors of the form 3*k+1.

1, 4, 16, 28, 80, 112, 320, 280, 784, 560, 1600, 1120, 10000, 2240, 3920, 2800, 25600, 5600, 1310720, 6160, 15680, 11200, 48400, 12320, 110000, 70000, 39200, 24640, 6553600, 30800, 5368709120, 36400, 78400, 179200, 440000, 61600, 343597383680, 1210000, 490000, 80080

Offset: 1

Ilya Gutkovskiy, Jul 28 2023

nonn

Bert Dobbelaere, Table of n, a(n) for n = 1..200

Cf. A001817, A005179, A038547, A364583.

a(n) = my(k=1); while (sumdiv(k, d, (d%3)==1) != n, k++); k; \\ Michel Marcus, Jul 29 2023

More terms from Bert Dobbelaere, Jul 31 2023

A364433 Numbers with multiplicities of primes per mod 3 residue in nonincreasing order.

Original entry on oeis.org

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

David A. Corneth, Aug 06 2023

nonn

Terms of A364583 are in this sequence.

			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.

Cf. A000244, A025487, A364583.

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)))

cp's OEIS Frontend

A364582 a(n) is the least number with exactly n divisors of the form 3*k+1.

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