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
Robert Israel, Table of n, a(n) for n = 1..10000
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
KEYWORD
nonn
AUTHOR
Gus Wiseman, Apr 11 2019
STATUS
approved