A061985 -id:A061985 - cp's OEIS frontend

A061987 Number of times n-th distinct value is repeated in sequence b(k) = 1 + b(floor(k/2)) + b(floor(k/3)) with b(0) = 0, i.e., in A061984; also number of times n-th distinct row is repeated in square array T(n,k) = T(n-1,k) + T(n-1,floor(k/2)) + T(n-1,floor(k/3)) with T(0,0) = 1, i.e., in A061980.

1, 1, 1, 1, 2, 2, 1, 3, 4, 2, 6, 3, 5, 4, 12, 6, 10, 8, 9, 15, 12, 20, 16, 18, 30, 24, 27, 13, 32, 36, 60, 48, 54, 26, 64, 72, 81, 39, 96, 108, 52, 128, 144, 162, 78, 192, 216, 104, 139, 117, 288, 324, 156, 384, 432, 208, 278, 234, 576, 648, 312, 417, 351, 864, 416, 556

Offset: 0

Henry Bottomley, May 24 2001

nonn

For n > 0: a(n) = A003586(n+1) - A003586(n) and a(A084791(n)) = A084788(n).
Also number of times A160519(n+1) is repeated in A088468. - Reinhard Zumkeller, May 16 2009
In the 14th century Levi Ben Gerson proved that a(n) > 1 for all n > 6; see A003586, A235365, A235366, A236210. - Jonathan Sondow, Jan 20 2014

Reinhard Zumkeller, Table of n, a(n) for n = 0..100
Eric Weisstein's World of Mathematics, Smooth Number

import Data.List (group)
a061987 n = a061987_list !! n
a061987_list = map length $ group a061984_list
-- Reinhard Zumkeller, Jan 11 2014

a(n) = A061986(A061985(n)).

More terms from Reinhard Zumkeller, Jun 03 2003

A061984 a(n) = 1 + a([n/2]) + a([n/3]) with a(0) = 0.

Original entry on oeis.org

0, 1, 2, 3, 4, 4, 6, 6, 7, 8, 8, 8, 11, 11, 11, 11, 12, 12, 15, 15, 15, 15, 15, 15, 19, 19, 19, 20, 20, 20, 20, 20, 21, 21, 21, 21, 27, 27, 27, 27, 27, 27, 27, 27, 27, 27, 27, 27, 32, 32, 32, 32, 32, 32, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 37, 37, 37, 37, 37, 37, 37, 37, 47

Offset: 0

Henry Bottomley, May 24 2001

nonn

If n = 2^a*3^b, then a(n)-a(n-1) = C(a+b, a). - David Wasserman, Nov 17 2005

Reinhard Zumkeller, Table of n, a(n) for n = 0..10000

Cf. A061980, A061985, A061986, A061987.

Cf. A007731.

a061984 n = a061984_list !! n
a061984_list = 0 : map (+ 1) (zipWith (+)
   (map (a061984 . (`div` 2)) [1..]) (map (a061984 . (`div` 3)) [1..]))
-- Reinhard Zumkeller, Jan 11 2014

A061986 Number of times n appears in sequence b(k) = 1 + b(floor(k/2)) + b(floor(k/3)) with b(0) = 0, i.e., in A061984.

Original entry on oeis.org

1, 1, 1, 1, 2, 0, 2, 1, 3, 0, 0, 4, 2, 0, 0, 6, 0, 0, 0, 3, 5, 4, 0, 0, 0, 0, 0, 12, 0, 0, 0, 0, 6, 0, 0, 0, 10, 8, 0, 0, 0, 0, 0, 0, 0, 0, 0, 9, 15, 0, 0, 0, 0, 0, 12, 0, 0, 0, 0, 0, 0, 0, 0, 0, 20, 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 18, 0, 0, 0, 0, 30, 0, 0, 0, 0, 0, 0, 24, 0, 0, 0, 0, 0, 0

Offset: 0

Henry Bottomley, May 24 2001

nonn

If n is not in A061985 then a(n)=0, otherwise if n=A061985(m) then a(n) = A061987(m).

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A061984 a(n) = 1 + a([n/2]) + a([n/3]) with a(0) = 0.

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A061986 Number of times n appears in sequence b(k) = 1 + b(floor(k/2)) + b(floor(k/3)) with b(0) = 0, i.e., in A061984.

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