|
|
A185379
|
|
Product of exactly three distinct primes congruent to 1 mod 8 (A007519).
|
|
1
|
|
|
50881, 62033, 67609, 78761, 95489, 110449, 120377, 134521, 140233, 146761, 162401, 167977, 170017, 170969, 179129, 186337, 195857, 207281, 218161, 225913, 234889, 239513, 246041, 263177, 266377, 279497, 285073, 289153, 290321, 292009, 299081, 301801, 312953
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
OFFSET
|
1,1
|
|
COMMENTS
|
Subset of numbers that are divisible by exactly 3 primes (counted with multiplicity), also known as triprimes or 3-almost primes, A014612. Subset of {d = p_1 * p_2 * ... * p_m where p_i == 1 (mod 8), 1 <= i <= m are distinct primes} as occurs in Wei, p.2.
|
|
LINKS
|
|
|
FORMULA
|
|
|
EXAMPLE
|
|
|
MATHEMATICA
|
p = Select[Prime[Range[100]], Mod[#, 8] == 1 &]; Sort[Reap[Do[n = p[[i]] p[[j]] p[[k]]; If[n <= p[[1]] p[[2]] p[[-1]], Sow[n]], {i, 2, Length[p]}, {j, i - 1}, {k, j - 1}]][[2, 1]]]
|
|
PROG
|
(PARI) list(lim)=my(v=List(), u=v, t); forprime(p=2, lim\697, if(p%8==1, listput(u, p))); for(i=1, #u-2, for(j=i+1, #u-1, if(u[i]*u[j]*u[j+1]>lim, break); for(k=j+1, #u, t=u[i]*u[j]*u[k]; if(t>lim, break); listput(v, t)))); Set(v) \\ Charles R Greathouse IV, Jan 31 2017
|
|
CROSSREFS
|
|
|
KEYWORD
|
nonn,easy
|
|
AUTHOR
|
|
|
STATUS
|
approved
|
|
|
|