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A325198 Positive numbers whose maximum prime index minus minimum prime index is 2.

%I A325198 #14 Feb 28 2020 22:53:50
%S A325198 10,20,21,30,40,50,55,60,63,80,90,91,100,105,120,147,150,160,180,187,
%T A325198 189,200,240,247,250,270,275,300,315,320,360,385,391,400,441,450,480,
%U A325198 500,525,540,551,567,600,605,637,640,713,720,735,750,800,810,900,945
%N A325198 Positive numbers whose maximum prime index minus minimum prime index is 2.
%C A325198 Also Heinz numbers of integer partitions whose maximum minus minimum part is 2 (counted by A008805). The Heinz number of an integer partition (y_1,...,y_k) is prime(y_1)*...*prime(y_k).
%H A325198 Robert Israel, <a href="/A325198/b325198.txt">Table of n, a(n) for n = 1..10000</a>
%e A325198 The sequence of terms together with their prime indices begins:
%e A325198    10: {1,3}
%e A325198    20: {1,1,3}
%e A325198    21: {2,4}
%e A325198    30: {1,2,3}
%e A325198    40: {1,1,1,3}
%e A325198    50: {1,3,3}
%e A325198    55: {3,5}
%e A325198    60: {1,1,2,3}
%e A325198    63: {2,2,4}
%e A325198    80: {1,1,1,1,3}
%e A325198    90: {1,2,2,3}
%e A325198    91: {4,6}
%e A325198   100: {1,1,3,3}
%e A325198   105: {2,3,4}
%e A325198   120: {1,1,1,2,3}
%e A325198   147: {2,4,4}
%e A325198   150: {1,2,3,3}
%e A325198   160: {1,1,1,1,1,3}
%e A325198   180: {1,1,2,2,3}
%e A325198   187: {5,7}
%p A325198 N:= 1000: # for terms <= N
%p A325198 q:= 2: r:= 3:
%p A325198 Res:= NULL:
%p A325198 do
%p A325198   p:= q; q:= r; r:= nextprime(r);
%p A325198   if p*r > N then break fi;
%p A325198   for i from 1 do
%p A325198     pi:= p^i;
%p A325198     if pi*r > N then break fi;
%p A325198     for j from 0 do
%p A325198       piqj:= pi*q^j;
%p A325198       if piqj*r > N then break fi;
%p A325198       Res:= Res, seq(piqj*r^k,k=1 .. floor(log[r](N/piqj)))
%p A325198     od
%p A325198   od
%p A325198 od:
%p A325198 sort([Res]); # _Robert Israel_, Apr 12 2019
%t A325198 Select[Range[100],PrimePi[FactorInteger[#][[-1,1]]]-PrimePi[FactorInteger[#][[1,1]]]==2&]
%Y A325198 Positions of 2's in A243055.
%Y A325198 A061395(a(n)) - A055396((n)) = 2.
%Y A325198 Cf. A000961, A008805, A046660, A056239, A093641, A112798, A118914, A174090, A195086, A256617, A325180, A325197.
%K A325198 nonn
%O A325198 1,1
%A A325198 _Gus Wiseman_, Apr 11 2019