|
%I #6 Apr 24 2019 19:48:01
%S 1,1,1,2,1,3,1,4,2,5,1,6,1,7,3,8,1,6,1,10,5,11,1,12,2,13,4,14,1,9,1,
%T 16,7,17,3,12,1,19,11,20,1,15,1,22,6,23,1,24,2,10,13,26,1,12,5,28,17,
%U 29,1,18,1,31,10,32,7,21,1,34,19,15,1,24,1,37,6,38
%N Heinz number of the differences plus one of the integer partition with Heinz number n.
%C The Heinz number of an integer partition (y_1,...,y_k) is prime(y_1)*...*prime(y_k).
%C The only fixed point is 1 because otherwise the sequence decreases omega (A001222) by one.
%e The partition (3,2,2,1) with Heinz number 90 has differences plus one (2,1,2) with Heinz number 18, so a(90) = 18.
%t primeMS[n_]:=If[n==1,{},Flatten[Cases[FactorInteger[n],{p_,k_}:>Table[PrimePi[p],{k}]]]];
%t db[n_]:=Times@@Prime/@(1+Differences[primeMS[n]]);
%t Table[db[n],{n,100}]
%Y Positions of m's are A008578 (m = 1), A001248 (m = 2), A006094 (m = 3), A030078 (m = 4), A090076 (m = 5).
%Y Cf. A007294, A049988, A056239, A093641, A112798, A240026, A320466, A325328, A325351, A325360, A325361, A325368, A325405.
%K nonn
%O 1,4
%A _Gus Wiseman_, Apr 23 2019
|
