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 A325195 Difference between the length of the minimal triangular partition containing and the maximal triangular partition contained in the Young diagram of the integer partition with Heinz number n. 11
 0, 0, 1, 1, 2, 0, 3, 2, 1, 1, 4, 1, 5, 2, 1, 3, 6, 1, 7, 1, 2, 3, 8, 2, 2, 4, 2, 2, 9, 0, 10, 4, 3, 5, 2, 2, 11, 6, 4, 2, 12, 1, 13, 3, 1, 7, 14, 3, 3, 1, 5, 4, 15, 2, 3, 2, 6, 8, 16, 1, 17, 9, 1, 5, 4, 2, 18, 5, 7, 1, 19, 3, 20, 10, 1, 6, 3, 3, 21, 3, 3, 11 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,5 COMMENTS The Heinz number of an integer partition (y_1,...,y_k) is prime(y_1)*...*prime(y_k). LINKS EXAMPLE The partition (3,3) has Heinz number 25 and diagram   o o o   o o o containing maximal triangular partition   o o   o and contained in minimal triangular partition   o o o o   o o o   o o   o so a(25) = 4 - 2 = 2. MATHEMATICA primeptn[n_]:=If[n==1, {}, Reverse[Flatten[Cases[FactorInteger[n], {p_, k_}:>Table[PrimePi[p], {k}]]]]]; otb[ptn_]:=Min@@MapIndexed[#1+#2[[1]]-1&, Append[ptn, 0]]; otbmax[ptn_]:=Max@@MapIndexed[#1+#2[[1]]-1&, Append[ptn, 0]]; Table[otbmax[primeptn[n]]-otb[primeptn[n]], {n, 100}] CROSSREFS Cf. A046660, A065770, A071724, A243055, A325166, A325169, A325178, A325183, A325188, A325189, A325191, A325196, A325197, A325199, A325200. Sequence in context: A156776 A292108 A342176 * A026728 A241556 A242029 Adjacent sequences:  A325192 A325193 A325194 * A325196 A325197 A325198 KEYWORD nonn AUTHOR Gus Wiseman, Apr 11 2019 STATUS approved

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Last modified April 17 02:26 EDT 2021. Contains 343059 sequences. (Running on oeis4.)