The On-Line Encyclopedia of Integer Sequences (OEIS)

Revision History for A336941

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A336941

Number of strict chains of divisors starting with the superprimorial A006939(n) and ending with 1.
(history; published version)

#14 by Alois P. Heinz at Sun Aug 30 20:23:11 EDT 2020

STATUS

proposed

approved

#13 by Andrew Howroyd at Sun Aug 30 20:06:56 EDT 2020

STATUS

editing

proposed

#12 by Andrew Howroyd at Sun Aug 30 20:06:43 EDT 2020

PROG

(PARI) a(n)={my(sig=vector(n, i, i), m=vecsum(sig)); sum(k=0, m, prod(i=1, #sig, binomial(sig[i]+k-1, k-1))*sum(r=k, m, binomial(r, k)*(-1)^(r-k)))} \\ Andrew Howroyd, Aug 30 2020

#11 by Andrew Howroyd at Sun Aug 30 19:35:35 EDT 2020

DATA

1, 1, 8, 604, 691968, 16359233536, 10083474928244288, 195661337707783118840768, 139988400203593571474134024847360, 4231553868972506381329450624389969130848256, 6090860257621637852755610879241895108657182173073604608, 464479854191019594417264488167571483344961210693790188774166838214656

LINKS

Andrew Howroyd, <a href="/A336941/b336941.txt">Table of n, a(n) for n = 0..25</a>

EXTENSIONS

Terms a(8) and beyond from Andrew Howroyd, Aug 30 2020

STATUS

approved

editing

#10 by Alois P. Heinz at Sun Aug 23 15:36:21 EDT 2020

STATUS

proposed

approved

#9 by Gus Wiseman at Sat Aug 22 19:12:02 EDT 2020

STATUS

editing

proposed

#8 by Gus Wiseman at Fri Aug 21 15:55:48 EDT 2020

EXAMPLE

1|12/1

1|2|12

1|3|12

1|4|12

1|6|12

1|2|4|12

1|2|6|12

1|3|6|12

12/2/1

12/3/1

12/4/1

12/6/1

12/4/2/1

12/6/2/1

12/6/3/1

Discussion

Sat Aug 22

19:12

Gus Wiseman: correction A002033 -> A074206 pointed out by Jinyuan Wang

#7 by Gus Wiseman at Fri Aug 21 15:51:30 EDT 2020

FORMULA

a(n) = A002033(A006939A337070(n))/2 for n > 0.

a(n) = A074206(A006939(n)).

CROSSREFS

A337070 is the version ending with any divisor of A006939(n).

A002033 A074206 counts chains of divisors from n to 1.

Cf. A000142, A001055, A002033, A008480, A022559, A027423, A124010, A167865, A181796, A336417, A336420, A337069.

STATUS

approved

editing

#6 by Susanna Cuyler at Fri Aug 14 16:28:41 EDT 2020

STATUS

proposed

approved

#5 by Gus Wiseman at Fri Aug 14 04:16:57 EDT 2020

STATUS

editing

proposed