OFFSET
1,2
COMMENTS
A prime index of n is a number m such that prime(m) divides n.
The Heinz number of an integer partition (y_1,...,y_k) is prime(y_1)*...*prime(y_k), so these are Heinz numbers of integer partitions into distinct parts, no two differing by less than 3 (counted by A025157).
LINKS
Robert Israel, Table of n, a(n) for n = 1..10000
EXAMPLE
The sequence of terms together with their prime indices begins:
1: {}
2: {1}
3: {2}
5: {3}
7: {4}
11: {5}
13: {6}
14: {1,4}
17: {7}
19: {8}
22: {1,5}
23: {9}
26: {1,6}
29: {10}
31: {11}
33: {2,5}
34: {1,7}
37: {12}
38: {1,8}
39: {2,6}
MAPLE
filter:= proc(n) local F;
F:= ifactors(n)[2];
if ormap(t -> t[2]>1, F) then return false fi;
if nops(F) <= 1 then return true fi;
F:= map(numtheory:-pi, sort(map(t -> t[1], F)));
min(F[2..-1]-F[1..-2]) >= 3;
end proc:
select(filter, [$1..200]); # Robert Israel, Apr 08 2019
MATHEMATICA
Select[Range[100], Min@@Differences[Flatten[Cases[FactorInteger[#], {p_, k_}:>Table[PrimePi[p], {k}]]]]>2&]
CROSSREFS
KEYWORD
nonn
AUTHOR
Gus Wiseman, Apr 05 2019
STATUS
approved