Year-end appeal: Please make a donation to the OEIS Foundation to support ongoing development and maintenance of the OEIS. We are now in our 61st year, we have over 378,000 sequences, and we’ve reached 11,000 citations (which often say “discovered thanks to the OEIS”).
%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