A307730 a(n) = A307720(n) * A307720(n+1).

1, 2, 2, 3, 3, 3, 6, 4, 4, 4, 4, 6, 6, 6, 6, 6, 9, 9, 9, 9, 9, 9, 9, 9, 9, 12, 8, 8, 8, 8, 8, 8, 8, 8, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 15, 5, 5, 5, 5, 5, 7, 7, 7, 7, 7, 7, 7, 14, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 14, 14, 14, 14, 14, 14, 14

Offset: 1

Author

Rémy Sigrist, Apr 25 2019

Keywords

• nonn
• hear

Comments

For all positive integers n, n appears n times.

Examples

			The first terms in this sequence and in A307720 are:
  n   a(n)  A307720(n)
  --  ----  ----------
   1     1           1
   2     2           1
   3     2           2
   4     3           1
   5     3           3
   6     3           1
   7     6           3
   8     4           2
   9     4           2
  10     4           2
		

Links

• Rémy Sigrist, Table of n, a(n) for n = 1..25000
• Rémy Sigrist, Scatterplot of the first 10000000 terms
• Rémy Sigrist, PARI program for A307730
• N. J. A. Sloane, Table of n, a(n) for n = 1..999999

Crossrefs

Cf. A002024, A088178, A307720.

Cf. A348579 (indices of occurrence of each number), A348246 (first occurrence of each number), A348409 (last occurrence).

Programs

PARI

\\ See Links section.

Python

from itertools import islice
from collections import Counter
def A307730(): # generator of terms. Greedy algorithm
    c, b = Counter(), 1
    while True:
        k, kb = 1, b
        while c[kb] >= kb:
            k += 1
            kb += b
        c[kb] += 1
        b = k
        yield kb
A307730_list = list(islice(A307730(),100)) # Chai Wah Wu, Oct 21 2021