The OEIS is supported by the many generous donors to the OEIS Foundation.

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A325364 Heinz numbers of integer partitions whose differences (with the last part taken to be zero) are weakly decreasing. 14
 1, 2, 3, 4, 5, 6, 7, 8, 9, 11, 13, 15, 16, 17, 18, 19, 21, 23, 25, 27, 29, 30, 31, 32, 35, 37, 41, 43, 47, 49, 53, 54, 55, 59, 61, 64, 65, 67, 71, 73, 75, 77, 79, 81, 83, 89, 91, 97, 101, 103, 105, 107, 109, 113, 119, 121, 125, 127, 128, 131, 133, 137, 139 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 COMMENTS The Heinz number of an integer partition (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 (x, y, z) are (y - x, z - y). We adhere to this standard for integer partitions also even though they are always weakly decreasing. For example, the differences of (6,3,1) (with the last part taken to be 0) are (-3,-2,-1). The enumeration of these partitions by sum is given by A320509. LINKS Table of n, a(n) for n=1..63. Gus Wiseman, Sequences counting and ranking integer partitions by the differences of their successive parts. MATHEMATICA primeptn[n_]:=If[n==1, {}, Reverse[Flatten[Cases[FactorInteger[n], {p_, k_}:>Table[PrimePi[p], {k}]]]]]; Select[Range[100], GreaterEqual@@Differences[Append[primeptn[#], 0]]&] CROSSREFS Cf. A056239, A112798, A320348, A320466, A320509, A325327, A325361, A325364, A325367, A325389, A325390, A325397. Sequence in context: A050741 A285710 A305669 * A133810 A176615 A291453 Adjacent sequences: A325361 A325362 A325363 * A325365 A325366 A325367 KEYWORD nonn AUTHOR Gus Wiseman, May 02 2019 STATUS approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recents
The OEIS Community | Maintained by The OEIS Foundation Inc.

Last modified February 29 21:35 EST 2024. Contains 370428 sequences. (Running on oeis4.)