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 A258120 Number of Fibonacci numbers in the partition having Heinz number n. 1
 0, 1, 1, 2, 1, 2, 0, 3, 2, 2, 1, 3, 0, 1, 2, 4, 0, 3, 1, 3, 1, 2, 0, 4, 2, 1, 3, 2, 0, 3, 0, 5, 2, 1, 1, 4, 0, 2, 1, 4, 1, 2, 0, 3, 3, 1, 0, 5, 0, 3, 1, 2, 0, 4, 2, 3, 2, 1, 0, 4, 0, 1, 2, 6, 1, 3, 0, 2, 1, 2, 0, 5, 1, 1, 3, 3, 1, 2, 0, 5, 4 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,4 COMMENTS We define the Heinz number of a partition p = [p_1, p_2, ..., p_r] as Product(p_j-th prime, j=1...r) (concept used by Alois P. Heinz in A215366 as an "encoding" of a partition). For example, for the partition [1, 1, 2, 4, 10] we get 2*2*3*7*29 = 2436; consequently, a(2436) = 3. The subprogram B of the Maple program gives the partition having Heinz number n. a(m*n) = a(m)+a(n). LINKS Alois P. Heinz, Table of n, a(n) for n = 1..10000 EXAMPLE a(2)=1 because B(2)=[1]; a(3)=1 because B(3)=[2]; a(4)=2 because B(4)=[1,1]; a(28)=2 because B(28)=[1,1,4]. MAPLE with(numtheory): a := proc (n) local B, F, ct, q: B := proc (n) local nn, j, m; nn := op(2, ifactors(n)): for j to nops(nn) do m[j] := op(j, nn) end do: [seq(seq(pi(op(1, m[i])), q = 1 .. op(2, m[i])), i = 1 .. nops(nn))] end proc; F := {seq(combinat['fibonacci'](1+i), i = 1 .. max(B(n)))}: ct := 0; for q to nops(B(n)) do if member(B(n)[q], F) = true then ct := ct+1 else end if end do: ct end proc: seq(a(n), n = 1 .. 150); MATHEMATICA B[n_] := Module[{nn, j, m}, nn = FactorInteger[n]; For[j = 1, j <= Length[nn], j++, m[j] = nn[[j]]]; Flatten[ Table[ Table[ PrimePi[ m[i][[1]]], {q, 1, m[i][[2]]}], {i, 1, Length[nn]}]]]; a[n_] := Module[{F, ct, q}, F = Union @ Table[Fibonacci[1 + i], {i, 1, Max[ B[n]]}]; ct = 0; For[q = 1, q <= Length[B[n]], q++, If[MemberQ[F, B[n][[q]]], ct++]]; ct]; Table[a[n], {n, 1, 150}] (* Jean-François Alcover, Apr 25 2017, translated from Maple *) CROSSREFS Cf. A000045, A215366. Sequence in context: A332104 A238735 A356006 * A147786 A275019 A337835 Adjacent sequences: A258117 A258118 A258119 * A258121 A258122 A258123 KEYWORD nonn AUTHOR Emeric Deutsch, Jun 14 2015 STATUS approved

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Last modified March 20 22:04 EDT 2023. Contains 361391 sequences. (Running on oeis4.)