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

1,1

Comments

A subsequence of A157941.

Links

Table of n, a(n) for n=1..54.

Formula

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

Example

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.

Prog

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

Crossrefs

Sequence in context: A090738 A085103 A280968 * A308494 A087696 A293529

Adjacent sequences: A157937 A157938 A157939 * A157941 A157942 A157943

Keyword

nonn

Author

M. F. Hasler, Mar 10 2009

Status

approved