A057035 Numbers n such that n = p + q with n*p*q = primorial number (A002110) (p <= q, p > 0, q > 0).

2, 3, 5, 6, 10, 15, 21, 22, 35, 55, 182, 221, 231, 357, 442, 715, 1105, 1430, 2958, 23345, 106981, 144210, 219965, 226083, 496961

Offset

1,1

Comments

No further terms with n*p*q <= A002110(18). - Robert Israel, Aug 07 2017

Links

Table of n, a(n) for n=1..25.

Example

2 = 1 + 1 -> 2*1*1 = 2;
715 = 1 + 714 -> 715*714*1 = 510510 = 17*13*11*7*5*3*2;
1105 = 231 + 874 -> 1105*231*874 = 223092870 = 23*19*...*2;
496961 = 495726 + 1235 -> (17*23*31*41)*(2*3*7*11*29*37)*(5*13*19) = 41*37*...*2.

Maple

R:= 2:
for m from 1 to 13 do
  P:= {seq(ithprime(i), i=1..m)}:
  C:= combinat:-powerset(P) minus {{}, P};
  for s3 in C do
    z:= convert(s3, `*`);
    C3:= P minus s3;
    zp:= convert(C3, `*`);
    if 4*zp > z^2 then next fi;
    for s1 in combinat:-powerset(C3 minus {max(C3)}) do
      x:= convert(s1, `*`);
      y:= zp/x;
      if x + y = z then
        R:= R, z;
      fi
    od
  od
od:
sort(convert({R}, list)); # Robert Israel, Aug 07 2017

Crossrefs

Cf. A002110, A056600, A056602.

Sequence in context: A101475 A262931 A018524 * A243805 A018594 A018626

Adjacent sequences: A057032 A057033 A057034 * A057036 A057037 A057038

Keyword

nonn,more

Author

Naohiro Nomoto, Sep 10 2000

Extensions

5 more terms from Carlos Rivera, Nov 22 2000

Status

approved