A334215 -id:A334215 - cp's OEIS frontend

A334216 a(n) is the number of distinct terms in the n-th row of A334215.

1, 2, 2, 3, 2, 2, 2, 3, 3, 2, 2, 3, 2, 2, 2, 4, 2, 3, 2, 3, 2, 2, 2, 3, 3, 2, 3, 3, 2, 2, 2, 4, 2, 2, 2, 3, 2, 2, 2, 3, 2, 2, 2, 3, 3, 2, 2, 4, 3, 3, 2, 3, 2, 3, 2, 3, 2, 2, 2, 3, 2, 2, 3, 5, 2, 2, 2, 3, 2, 2, 2, 4, 2, 2, 3, 3, 2, 2, 2, 4, 4, 2, 2, 3, 2, 2, 2

Offset: 1

Rémy Sigrist, Apr 19 2020

nonn

Cf. A000005, A000267, A334215, A334217.

a(n) = { my (f=factor(n)); #Set(apply (k -> prod (i=1, #f~, f[i,1]^(f[i,2]\k)), [1..1+if (n==1, 0, vecmax(f[,2]~))])) }

a(n) <= A000005(n).

a(p^k) = A000267(k) for any k >= 0 and prime number p.

A334217 Irregular table T(n, k) read by rows, n > 0 and k = 1..A334216(n); n-th row corresponds to distinct terms of n-th row of A334215, in ascending order.

Original entry on oeis.org

1, 1, 2, 1, 3, 1, 2, 4, 1, 5, 1, 6, 1, 7, 1, 2, 8, 1, 3, 9, 1, 10, 1, 11, 1, 2, 12, 1, 13, 1, 14, 1, 15, 1, 2, 4, 16, 1, 17, 1, 3, 18, 1, 19, 1, 2, 20, 1, 21, 1, 22, 1, 23, 1, 2, 24, 1, 5, 25, 1, 26, 1, 3, 27, 1, 2, 28, 1, 29, 1, 30, 1, 31, 1, 2, 4, 32, 1, 33

Offset: 1

Rémy Sigrist, Apr 19 2020

			The first rows are:
  n     n-th row
  --    -------------
   1    [1]
   2    [1, 2]
   3    [1, 3]
   4    [1, 2, 4]
   5    [1, 5]
   6    [1, 6]
   7    [1, 7]
   8    [1, 2, 8]
   9    [1, 3, 9]
  10    [1, 10]
  11    [1, 11]
  12    [1, 2, 12]
  13    [1, 13]
  14    [1, 14]
  15    [1, 15]
  16    [1, 2, 4, 16]

Cf. A000188, A261969, A334215, A334216.

row(n) = { my (f=factor(n)); Set(apply (k -> prod (i=1, #f~, f[i,1]^(f[i,2]\k)), [1..1+if (n==1, 0, vecmax(f[,2]~))])) }

T(n, 1) = 1.
T(n, 2) = A261969(n) for any n > 1.
T(n, A334216(n)-1) = A000188(n) for any n > 1.
T(n, A334216(n)) = n.

cp's OEIS Frontend

A334216 a(n) is the number of distinct terms in the n-th row of A334215.

Views

Author

Keywords

Crossrefs

Programs

PARI

Formula