A255911 a(n) is the smallest natural number such that A002182(n) = a(n) * A002182(n - i) for some i > 0, where A002182 is the sequence of highly composite numbers.

2, 2, 3, 2, 2, 3, 2, 5, 2, 3, 2, 2, 2, 7, 7, 2, 2, 2, 3, 2, 2, 2, 5, 11, 3, 2, 2, 3, 2, 2, 2, 5, 2, 3, 2, 2, 13, 13, 2, 2, 2, 5, 2, 3, 2, 2, 3, 2, 2, 2, 3, 17, 2, 17, 2, 3, 2, 2, 3, 2, 2, 2, 3, 19, 2, 2, 2, 3, 2, 19, 2, 5, 2, 2, 2, 3, 2, 2, 2, 2, 7, 23, 7

Offset

2,1

Comments

Each highly composite number hcn(n) (except the first) in the sequence A002182 is a product of a relatively small natural number and a preceding highly composite number hcn(n - i) in A002182.

The first nonprime term in A255911 is a(698) = 10.

Links

Peter McGavin, Table of n, a(n) for n = 2..1000

Example

In A002182, hcn(5),hcn(6),hcn(7) = 12,24,36.
We have hcn(6) = 2 * hcn(5), therefore a(6) = 2.
hcn(6) is not a divisor of hcn(7), but hcn(7) = 3 * hcn(5), therefore a(7) = 3.

Maple

# Uses "http://oeis.org/wiki/User:R._J._Mathar/transforms3" to read a b-file
read("transforms3");
hcn:=BFILETOLIST("b002182.txt"):
a:=[]:
for i from 2 to nops(hcn) do \
  j := i - 1: \
  while (j > 0 and hcn[i] mod hcn[j] <> 0) do \
    j := j - 1:
  end do: \
  a := [op(a), hcn[i] / hcn[j]]: \
end do:
a;
# Peter McGavin, Mar 15 2015

Prog

(C)
/* program fragment */
/* All variables are int */
/* Given the sequence A002182 already is in hcn[0..n-1] */
for (i = 1; i < n; i++) {
   for (j = i - 1; j >= 0 && hcn[i] % hcn[j] != 0; --j)
     /* do nothing */ ;
   printf (", %d", hcn[i] / hcn[j]);
}
/* Peter McGavin, Mar 10 2015 */
(PARI) lista(nn) = {v = readvec("c:/gp/bfiles/b002182.txt"); for (n=2, nn, k = 0; for (i=1, n-1, if (type(kv = v[n]/v[i]) == "t_INT", if (k==0, k = kv, k = min(k, kv)); ); ); print1(k, ", "); ); } \\ Michel Marcus, Mar 11 2015
(Python)
from sympy import divisor_count
A002182_list, A255911_list, count, m = [], [], 0, 0
for i in range(1, 10**6):
....d = divisor_count(i)
....if d > m:
........m = d
........A002182_list.append(i)
........for j in range(count-1, -1, -1):
............q, r = divmod(i, A002182_list[j])
............if not r:
................A255911_list.append(q)
................break
........count += 1 # Chai Wah Wu, Mar 23 2015

Crossrefs

Cf. A002182.

Sequence in context: A270516 A099318 A187128 * A091382 A127808 A127809

Adjacent sequences: A255908 A255909 A255910 * A255912 A255913 A255914

Keyword

nonn

Author

Peter McGavin, Mar 10 2015

Status

approved