A368309 Numbers k such that all primes dividing the k-th composite number divide k as well.

6, 15, 20, 24, 30, 96, 168, 189, 300, 348, 414, 510, 660, 1260, 1458, 1738, 2214, 2805, 3010, 3984, 4330, 4485, 5798, 5859, 5880, 6360, 7364, 7420, 7656, 8245, 8770, 9096, 10340, 10818, 12882, 12925, 13108, 23944, 33852, 37134, 44100, 45960, 47740, 49110, 55260, 55518, 58140, 63336, 73910, 76890

Offset

1,1

Comments

Numbers k such that k == 0 (mod p) for all primes p dividing A002808(k).

Numbers k such that A137924(k) = 1.

Numbers k such that k == 0 (mod A007947(A002808(k))).

Links

Table of n, a(n) for n=1..50.

Example

a(4) = 24 is a term because A002808(24), the 24th composite number, is 36, and the primes 2 and 3 that divide 36 also divide 24.

Maple

R:= NULL: n:= 0: count:= 0:
for i from 4 while count < 100 do
  if not isprime(i) then
    n:= n+1;
    if map(t -> n mod t, numtheory:-factorset(i)) = {0} then
       count:= count+1; R:= R, n;
    fi
  fi
od:
R;

Crossrefs

Cf. A002808, A007947, A137924.

Sequence in context: A045848 A335268 A294651 * A044439 A348866 A128253

Adjacent sequences: A368306 A368307 A368308 * A368310 A368311 A368312

Keyword

nonn

Author

Robert Israel, Dec 20 2023

Status

approved