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

0,1

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...

Links

Table of n, a(n) for n=0..50.

Formula

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

Example

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

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 *)

Prog

(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.

Crossrefs

Sequence in context: A157942 A122786 A092630 * A062002 A090419 A209799

Adjacent sequences: A079139 A079140 A079141 * A079143 A079144 A079145

Keyword

nonn

Author

Cino Hilliard, Dec 26 2002

Status

approved