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Numbers k such that all primes dividing the k-th composite number divide k as well.
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%I #4 Dec 30 2023 23:15:39

%S 6,15,20,24,30,96,168,189,300,348,414,510,660,1260,1458,1738,2214,

%T 2805,3010,3984,4330,4485,5798,5859,5880,6360,7364,7420,7656,8245,

%U 8770,9096,10340,10818,12882,12925,13108,23944,33852,37134,44100,45960,47740,49110,55260,55518,58140,63336,73910,76890

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

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

%C Numbers k such that A137924(k) = 1.

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

%e 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.

%p R:= NULL: n:= 0: count:= 0:

%p for i from 4 while count < 100 do

%p if not isprime(i) then

%p n:= n+1;

%p if map(t -> n mod t, numtheory:-factorset(i)) = {0} then

%p count:= count+1; R:= R, n;

%p fi

%p fi

%p od:

%p R;

%Y Cf. A002808, A007947, A137924.

%K nonn

%O 1,1

%A _Robert Israel_, Dec 20 2023