The On-Line Encyclopedia of Integer Sequences (OEIS)

Revision History for A325770

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A325770

Number of distinct nonempty contiguous subsequences of the integer partition with Heinz number n.
(history; published version)

#11 by Susanna Cuyler at Sat Jun 27 21:27:19 EDT 2020

STATUS

proposed

approved

#10 by Gus Wiseman at Sat Jun 27 16:50:27 EDT 2020

STATUS

editing

proposed

#9 by Gus Wiseman at Sat Jun 27 16:50:19 EDT 2020

CROSSREFS

Cf. A002865, A103295, A108917, A112798, A124771, A126796, A276024, A325765, A325768, A325769, A335519, A335838.

#8 by Gus Wiseman at Sat Jun 27 16:40:05 EDT 2020

CROSSREFS

Cf. A002865, A103295, A108917, A112798, A124771, A126796, A276024, A325765, A325768, A325769, A335519, A335838.

#7 by Gus Wiseman at Sat Jun 27 06:34:39 EDT 2020

EXTENSIONS

Name corrected by Gus Wiseman, Jun 27 2020

#6 by Gus Wiseman at Sat Jun 27 06:32:35 EDT 2020

CROSSREFS

Cf. A000041, A002033, A003022, A103295, A103300, A108917, A112798, A124771, A126796, A143823, A143824, A169942, A276024, A325684, A325764, A325765, A325768, A325769, A335519, A335838.

#5 by Gus Wiseman at Sat Jun 27 06:25:47 EDT 2020

NAME

Number of distinct consecutive subsequence-sums nonempty contiguous subsequences of the integer partition with Heinz number n.

FORMULA

a(n) = A335519(n) - 1.

EXAMPLE

The a(84) = 9 distinct consecutive subsequence-sums nonempty contiguous subsequences of (4,2,1,1) are (1, ), (2, 3, ), (4, 6, 7, 8, so a(84) = 7. Subsequences realizing these sums are , (1,1), (2,1), (4), (,2,1), (4,2,1,1), (4,2,1), (4,2,1,1).

CROSSREFS

Cf. A000041, A002033, A003022, A103295, A103300, A108917, A112798, A124771, A126796, A143823, A143824, A169942, A276024, A325684, A325764, A325765, A325768, A325769, A335519, A335838.

STATUS

approved

editing

#4 by Susanna Cuyler at Tue May 21 22:05:47 EDT 2019

STATUS

proposed

approved

#3 by Gus Wiseman at Mon May 20 18:36:03 EDT 2019

STATUS

editing

proposed

#2 by Gus Wiseman at Mon May 20 15:26:23 EDT 2019

NAME

allocated for Gus WisemanNumber of distinct consecutive subsequence-sums of the integer partition with Heinz number n.

DATA

0, 1, 1, 2, 1, 3, 1, 3, 2, 3, 1, 5, 1, 3, 3, 4, 1, 5, 1, 5, 3, 3, 1, 7, 2, 3, 3, 5, 1, 6, 1, 5, 3, 3, 3, 8, 1, 3, 3, 7, 1, 6, 1, 5, 5, 3, 1, 9, 2, 5, 3, 5, 1, 7, 3, 7, 3, 3, 1, 9, 1, 3, 5, 6, 3, 6, 1, 5, 3, 6, 1, 11, 1, 3, 5, 5, 3, 6, 1, 9, 4, 3, 1, 9, 3, 3, 3

OFFSET

1,4

COMMENTS

After a(1) = 0, first differs from A305611 at a(42) = 6, A305611(42) = 7.

The Heinz number of an integer partition (y_1,...,y_k) is prime(y_1)*...*prime(y_k).

EXAMPLE

The distinct consecutive subsequence-sums of (4,2,1,1) are 1, 2, 3, 4, 6, 7, 8, so a(84) = 7. Subsequences realizing these sums are (1), (2), (4), (2,1), (4,2), (4,2,1), (4,2,1,1).

MATHEMATICA

Table[Length[Union[ReplaceList[If[n==1, {}, Flatten[Cases[FactorInteger[n], {p_, k_}:>Table[PrimePi[p], {k}]]]], {___, s__, ___}:>{s}]]], {n, 30}]

CROSSREFS

Cf. A000041, A002033, A003022, A103295, A103300, A108917, A143823, A143824, A169942, A276024, A325684, A325764, A325765, A325768, A325769.

KEYWORD

allocated

nonn

AUTHOR

Gus Wiseman, May 20 2019

STATUS

approved

editing