OFFSET
1,1
COMMENTS
Sphenic numbers are products of three distinct primes. Semiprimes are products of two primes, not necessarily distinct.
Contains A215217.
LINKS
Robert Israel, Table of n, a(n) for n = 1..8683
EXAMPLE
102=2*3*17 and 105=3*5*7 are sphenic numbers, i.e., products of three distinct primes, and neither 103 (a prime) nor 104=2^3*13 is a semiprime, so 102 is in the sequence.
MAPLE
N:= 10000: # to get all terms where the next sphenic number <= N
Sphenics:= select(t -> (map(s->s[2], ifactors(t)[2])=[1, 1, 1]), {$1..N}):
Primes:= select(isprime, {2, seq(2*i+1, i=1..floor(N/2))}):
Semiprimes:= {seq(seq(p*q, q=select(`<=`, Primes, N/p)), p=Primes)}:
map(proc(i) if nops(Semiprimes intersect {$Sphenics[i]..Sphenics[i+1]}) = 0 then Sphenics[i] else NULL fi end proc, [$1..nops(Sphenics)-1]);
MATHEMATICA
sw = Switch[FactorInteger[#][[All, 2]], {1, 1}, {#, 2}, {1, 1, 1}, {#, 3}, _, Nothing]& /@ Range[10^4];
sp = SequencePosition[sw, {{_, 3}, {_, 3}}][[All, 1]];
sw[[sp]][[All, 1]] (* Jean-François Alcover, Sep 26 2020 *)
CROSSREFS
KEYWORD
nonn
AUTHOR
Robert Israel, Aug 13 2014
STATUS
approved