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

1,2

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

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 *)

Prog

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

Crossrefs

Cf. A097974.

Sequence in context: A323021 A026235 A086281 * A130088 A369033 A078834

Adjacent sequences: A097972 A097973 A097974 * A097976 A097977 A097978

Keyword

nonn

Author

Leroy Quet, Sep 07 2004

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

Status

approved