The On-Line Encyclopedia of Integer Sequences (OEIS)

Revision History for A348531 (Bold, blue-underlined text is an addition; faded, red-underlined text is a ~~deletion~~.)
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A348531

Number of partitions of n into 3 parts where at least one of the parts divides the product of the other two.
(history; published version)

#16 by Wesley Ivan Hurt at Thu Oct 21 22:40:35 EDT 2021

STATUS

proposed

approved

#15 by Michael De Vlieger at Thu Oct 21 21:36:38 EDT 2021

STATUS

editing

proposed

#14 by Michael De Vlieger at Thu Oct 21 21:36:32 EDT 2021

MATHEMATICA

Block[{c}, c[n_] := 1 - Ceiling[n] + Floor[n]; Array[Sum[Sum[Sign[c[i*(# - i - j)/j] + c[j*(# - i - j)/i] + c[i*j/(# - i - j)]], {i, j, Floor[(# - j)/2]}], {j, Floor[#/3]} ] &, 67]] (* Michael De Vlieger, Oct 21 2021 *)

STATUS

proposed

editing

#13 by Wesley Ivan Hurt at Thu Oct 21 13:16:57 EDT 2021

STATUS

editing

proposed

#12 by Wesley Ivan Hurt at Thu Oct 21 13:16:45 EDT 2021

FORMULA

a(n) = Sum_{j=1..floor(n/3)} Sum_{i=j..floor((n-j)/2)} sign( c(i*(n-i-j)/j) + c(j*(n-i-j)/i) + c(i*j/(n-i-j)) ), where c(n) = 1 - ceiling(n) + floor(n).

#11 by Wesley Ivan Hurt at Thu Oct 21 13:15:56 EDT 2021

NAME

allocated for Wesley Ivan HurtNumber of partitions of n into 3 parts where at least one of the parts divides the product of the other two.

DATA

0, 0, 1, 1, 2, 3, 4, 5, 7, 7, 10, 10, 14, 14, 17, 17, 22, 20, 28, 25, 29, 30, 38, 32, 43, 40, 45, 43, 57, 45, 62, 56, 62, 63, 70, 61, 84, 74, 81, 74, 98, 78, 108, 92, 95, 102, 120, 95, 127, 109, 123, 116, 149, 118, 142, 129, 145, 147, 173, 126, 182, 163, 164, 164, 184, 158, 211

OFFSET

1,5

LINKS

<a href="/index/Par#part">Index entries for sequences related to partitions</a>

FORMULA

a(n) = Sum_{j=1..floor(n/3)} Sum_{i=j..floor((n-j)/2)} sign( c(i*(n-i-j)/j) + c(j*(n-i-j)/i) + c(i*j/(n-i-j)) ), where c(n) = 1-ceiling(n)+floor(n).

EXAMPLE

a(9) = 7; All of the partitions of 9 (into 3 such parts) satisfy these conditions. They are (1,1,7), (1,2,6), (1,3,5), (1,4,4), (2,2,5), (2,3,4) and (3,3,3).

a(10) = 7; The partitions of 10 into 3 such parts are (1,1,8), (1,2,7), (1,3,6), (1,4,5), (2,2,6), (2,4,4) and (3,3,4).

KEYWORD

allocated

nonn

AUTHOR

Wesley Ivan Hurt, Oct 21 2021

STATUS

approved

editing

#10 by Wesley Ivan Hurt at Thu Oct 21 13:15:56 EDT 2021

NAME

allocated for Wesley Ivan Hurt

KEYWORD

recycled

allocated

#9 by Alois P. Heinz at Thu Oct 21 12:36:13 EDT 2021

STATUS

editing

approved

#8 by Alois P. Heinz at Thu Oct 21 12:35:22 EDT 2021

NAME

Primes followed by gap 400.

DATA

47203303159

OFFSET

1,1

COMMENTS

recycle

KEYWORD

nonn,changed

recycled

AUTHOR

Zak Seidov, Oct 21 2021

STATUS

proposed

editing

Discussion

Thu Oct 21

12:35

Alois P. Heinz: withdrawn by author ...

#7 by Zak Seidov at Thu Oct 21 12:14:18 EDT 2021

STATUS

editing

proposed

Discussion

Thu Oct 21

12:28

Michel Marcus: çà, çà me gonfle !!!