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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. 1
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 (list; graph; refs; listen; history; text; internal format)
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

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Last modified September 30 18:12 EDT 2020. Contains 337440 sequences. (Running on oeis4.)