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A238503
Numbers of the form pq + pr + ps + qr + qs + rs where p, q, r, and s are distinct primes.
1
101, 141, 161, 173, 197, 201, 213, 221, 236, 241, 245, 261, 266, 269, 297, 317, 321, 325, 326, 333, 341, 350, 356, 365, 373, 377, 381, 389, 393, 401, 404, 413, 416, 426, 429, 441, 453, 461, 464, 465, 466, 476, 481, 485, 488, 493, 501, 505, 506
OFFSET
1,1
COMMENTS
Numbers of the form e2(p, q, r, s) for distinct primes p, q, r, s where e2 is the elementary symmetric polynomial of degree 2. Other sequences are obtained with different numbers of distinct primes and degrees: A000040 for 1 prime, A038609 and A006881 for 2 primes, A124867, A238397, and A007304 for 3 primes.
What is the density of this sequence, and is it less than 1? There are 701917 terms below a million and 7042080 below 10^7.
There are 70307093 terms below 10^8. - Charles R Greathouse IV, Jun 14 2017
LINKS
Charles R Greathouse IV, Table of n, a(n) for n = 1..10000
EXAMPLE
101 = 2*3 + 2*5 + 2*7 + 3*5 + 3*7 + 5*7.
MATHEMATICA
pqrs[{p_, q_, r_, s_}]:=Total[Times@@@Subsets[{p, q, r, s}, {2}]]; Take[ Flatten[ pqrs/@Subsets[Prime[Range[20]], {4}]]//Union, 50] (* Harvey P. Dale, Jan 17 2021 *)
PROG
(PARI) list(n)=my(v=List()); forprime(s=7, (n-31)\10, forprime(r=5, min((n-6-5*s)\(s+5), s-2), forprime(q=3, min((n-2*r-2*s-r*s)\(s+r+2), r-2), my(S=q+r+s, P=q*r+r*s+q*s); forprime(p=2, min((n-P)\S, q-1), listput(v, p*S+P))))); Set(v)
(PARI) list(n)=my(v=vectorsmall(n), u=List()); forprime(s=7, (n-31)\10, forprime(r=5, min((n-6-5*s)\(s+5), s-2), forprime(q=3, min((n-2*r-2*s-r*s)\(s+r+2), r-2), my(S=q+r+s, P=q*r+r*s+q*s); forprime(p=2, min((n-P)\S, q-1), v[p*S+P]=1)))); for(i=1, n, if(v[i], listput(u, i))); Vec(u)
CROSSREFS
Cf. A238397.
Sequence in context: A050672 A122531 A141871 * A050806 A243890 A129563
KEYWORD
nonn
AUTHOR
STATUS
approved