A325390 Heinz number of the negated differences plus one of the integer partition with Heinz number n (with the last part taken to be 0).

1, 3, 5, 6, 7, 9, 11, 12, 10, 15, 13, 18, 17, 21, 15, 24, 19, 18, 23, 30, 25, 33, 29, 36, 14, 39, 20, 42, 31, 27, 37, 48, 35, 51, 21, 36, 41, 57, 55, 60, 43, 45, 47, 66, 30, 69, 53, 72, 22, 30, 65, 78, 59, 36, 35, 84, 85, 87, 61, 54, 67, 93, 50, 96, 49, 63, 71

Offset

1,2

Comments

The Heinz number of a positive integer sequence (y_1,...,y_k) is prime(y_1)*...*prime(y_k).

The differences of a sequence are defined as if the sequence were increasing, so for example the differences of (6,3,1) (with the last part taken to be 0) are (-3,-2,-1).

Links

Table of n, a(n) for n=1..67.

Gus Wiseman, Sequences counting and ranking integer partitions by the differences of their successive parts.

Example

The Heinz number of (6,3,1) is 130, and its negated differences plus one are (4,3,2), which has Heinz number 105, so a(130) = 105.

Mathematica

primeptn[n_]:=If[n==1, {}, Reverse[Flatten[Cases[FactorInteger[n], {p_, k_}:>Table[PrimePi[p], {k}]]]]];
Table[Times@@Prime/@(1-Differences[Append[primeptn[n], 0]]), {n, 100}]

Crossrefs

Number of appearances of n is A325392(n).

Positions of squarefree numbers are A325367.

Cf. A007294, A007862, A056239, A112798, A320509, A325324, A325327, A325351, A325352, A325362, A325364, A325460, A325461.

Sequence in context: A247523 A169957 A165712 * A296365 A291166 A333228

Adjacent sequences: A325387 A325388 A325389 * A325391 A325392 A325393

Keyword

nonn

Author

Gus Wiseman, May 02 2019

Status

approved