A097975 a(n) is the prime divisor of n which is >= sqrt(n), or 0 if there is no such prime divisor.

0, 2, 3, 2, 5, 3, 7, 0, 3, 5, 11, 0, 13, 7, 5, 0, 17, 0, 19, 5, 7, 11, 23, 0, 5, 13, 0, 7, 29, 0, 31, 0, 11, 17, 7, 0, 37, 19, 13, 0, 41, 7, 43, 11, 0, 23, 47, 0, 7, 0, 17, 13, 53, 0, 11, 0, 19, 29, 59, 0, 61, 31, 0, 0, 13, 11, 67, 17, 23, 0, 71, 0, 73, 37, 0, 19, 11, 13, 79, 0, 0, 41, 83

Offset: 1

Author

Leroy Quet, Sep 07 2004

Keywords

• nonn

Comments

Sequence also is the sum of distinct prime divisors of n which are >= sqrt(n). At most one prime divisor of n is >= square root of n.

Links

• Diana Mecum, Table of n, a(n) for n = 1..1000

Crossrefs

Cf. A097974.

Programs

Mathematica

Do[l = Select[Select[Divisors[n], PrimeQ], # >= Sqrt[n]&]; If[Length[l] == 0, Print[0], Print[l[[1]]]], {n, 1, 50}] (* Ryan Propper, Jul 24 2005 *)
Array[Select[FactorInteger[#][[All, 1]], Function[p, p >= Sqrt@ #]] /. {{} -> {0}, {1} -> {0}} &, 83][[All, 1]] (* Michael De Vlieger, Dec 22 2017 *)

PARI

a(n) = sumdiv(n, d, if (isprime(d) && (d^2 >= n), d)); \\ Michel Marcus, Dec 23 2017

Extensions

More terms from Ryan Propper, Jul 24 2005

More terms from Stefan Steinerberger, Jan 21 2006

Further terms from Diana L. Mecum, Jun 15 2007