A157940 Numbers n divisible by the largest prime <= sqrt(n) which are not in A001248 (primes squared) or A006094 (product of two consecutive primes).

8, 12, 18, 24, 30, 40, 45, 56, 63, 70, 84, 98, 105, 112, 132, 154, 165, 182, 195, 208, 234, 260, 273, 286, 306, 340, 357, 380, 399, 418, 456, 475, 494, 513, 552, 575, 598, 621, 644, 690, 736, 759, 782, 805, 828, 870, 928, 957, 992, 1023, 1054, 1085, 1116, 1178

Offset: 1

Author

M. F. Hasler, Mar 10 2009

Keywords

• nonn

Comments

A subsequence of A157941.

Examples

			For numbers less than 4 the definition does not make sense, since there's no prime < 2=sqrt(4).
a(1)=8 which is divisible by 2 = precprime(sqrt(8)) and neither a prime squared (as would be 4 and 9) nor product of consecutive primes.
5 and 7 are not in this sequence, since not a multiple of 2=precprime(sqrt(5)) =precprime(sqrt(7)).
6 is not in the sequence, since it is the product of 2=precprime(sqrt(6)) and the following prime, 3. For the same reason, 15 is excluded.
		

Programs

PARI

for( n=5,1999, n % precprime(sqrtint(n)) & next; n % nextprime(sqrtint(n-1)+1) & print1(n","))

Formula

A157940 = A157942 \ A157936 = A157941 \ A006094, where A157941 = A157942 \ A001248.