A079143 Numbers divisible by prime ceilings of their square roots + 1.

2, 4, 6, 9, 20, 25, 42, 49, 110, 121, 156, 169, 272, 289, 342, 361, 506, 529, 812, 841, 930, 961, 1332, 1369, 1640, 1681, 1806, 1849, 2162, 2209, 2756, 2809, 3422, 3481, 3660, 3721, 4422, 4489, 4970, 5041, 5256, 5329, 6162, 6241, 6806, 6889, 7832, 7921

Offset: 1

Author

Cino Hilliard, Dec 26 2002

Keywords

• easy
• nonn

Comments

n is in the sequence if r=ceiling(sqrt(n)) is prime and r divides n.

Union of the 2 sequences A001248={p^2} and A036689={p(p-1)} for p prime.

Sum of the reciprocals = 1.225...

Examples

			930 is in the sequence because ceiling(sqrt(930)) = 31 and 930/31 = 30.
		

Programs

Mathematica

Flatten[ #(#-{1, 0})&/@Prime/@Range[30]]
a[n_] := (p=Prime[Ceiling[n/2]])(p-Mod[n, 2])

PARI

ipsqrt(n) = { sr= 0; for(x=1,n, v = ceil(sqrt(x)); if(isprime(v) && x%v == 0, print1(x" "); sr+=1.0/x; ); ); print(); print(sr); } \\ numbers divisible by the prime ceilings of their square roots.

Formula

a(n) = prime(ceiling(n/2))*(prime(ceiling(n/2)) - (n mod 2))