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A325198
Positive numbers whose maximum prime index minus minimum prime index is 2.
5
10, 20, 21, 30, 40, 50, 55, 60, 63, 80, 90, 91, 100, 105, 120, 147, 150, 160, 180, 187, 189, 200, 240, 247, 250, 270, 275, 300, 315, 320, 360, 385, 391, 400, 441, 450, 480, 500, 525, 540, 551, 567, 600, 605, 637, 640, 713, 720, 735, 750, 800, 810, 900, 945
OFFSET
1,1
COMMENTS
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).
LINKS
EXAMPLE
The sequence of terms together with their prime indices begins:
10: {1,3}
20: {1,1,3}
21: {2,4}
30: {1,2,3}
40: {1,1,1,3}
50: {1,3,3}
55: {3,5}
60: {1,1,2,3}
63: {2,2,4}
80: {1,1,1,1,3}
90: {1,2,2,3}
91: {4,6}
100: {1,1,3,3}
105: {2,3,4}
120: {1,1,1,2,3}
147: {2,4,4}
150: {1,2,3,3}
160: {1,1,1,1,1,3}
180: {1,1,2,2,3}
187: {5,7}
MAPLE
N:= 1000: # for terms <= N
q:= 2: r:= 3:
Res:= NULL:
do
p:= q; q:= r; r:= nextprime(r);
if p*r > N then break fi;
for i from 1 do
pi:= p^i;
if pi*r > N then break fi;
for j from 0 do
piqj:= pi*q^j;
if piqj*r > N then break fi;
Res:= Res, seq(piqj*r^k, k=1 .. floor(log[r](N/piqj)))
od
od
od:
sort([Res]); # Robert Israel, Apr 12 2019
MATHEMATICA
Select[Range[100], PrimePi[FactorInteger[#][[-1, 1]]]-PrimePi[FactorInteger[#][[1, 1]]]==2&]
CROSSREFS
Positions of 2's in A243055.
A061395(a(n)) - A055396((n)) = 2.
Sequence in context: A210589 A296714 A297147 * A098165 A104801 A364325
KEYWORD
nonn
AUTHOR
Gus Wiseman, Apr 11 2019
STATUS
approved