A079142 Numbers divisible by prime integer parts of their square roots.

4, 6, 8, 9, 12, 15, 25, 30, 35, 49, 56, 63, 121, 132, 143, 169, 182, 195, 289, 306, 323, 361, 380, 399, 529, 552, 575, 841, 870, 899, 961, 992, 1023, 1369, 1406, 1443, 1681, 1722, 1763, 1849, 1892, 1935, 2209, 2256, 2303, 2809, 2862, 2915, 3481, 3540, 3599

Offset: 0

Author

Cino Hilliard, Dec 26 2002

Keywords

• nonn

Comments

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

Union of the 3 sequences A001248={p^2}, A036690={p(p+1)} and {p(p+2)} for p prime.

The sum of the reciprocals = 1.04...

Examples

			56 is in the sequence because floor(sqrt(56)) = 7 is prime and 7 divides 56.
		

Programs

Mathematica

Flatten[ #(#+{0, 1, 2})&/@Prime/@Range[20]]
a[n_] := (p=Prime[Floor[n/3+1]])(p+Mod[n, 3])
dpipQ[n_]:=Module[{c=Floor[Sqrt[n]]},PrimeQ[c]&&Divisible[n,c]]; Select[Range[ 4000],dpipQ] (* Harvey P. Dale, Mar 10 2013 *)

PARI

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

Formula

a(n) = prime(floor(n/3+1))*(prime(floor(n/3+1)) + (n mod 3))