A134875 - OEIS

A134875

a(n)=the smallest sum of two nontrivial divisors of n, if any, whose product equals n; otherwise, a(n)=n.

1, 2, 3, 4, 5, 5, 7, 6, 6, 7, 11, 7, 13, 9, 8, 8, 17, 9, 19, 9, 10, 13, 23, 10, 10, 15, 12, 11, 29, 11, 31, 12, 14, 19, 12, 12, 37, 21, 16, 13, 41, 13, 43, 15, 14, 25, 47, 14, 14, 15, 20, 17, 53, 15, 16, 15, 22, 31, 59, 16, 61, 33, 16, 16, 18, 17, 67, 21, 26, 17, 71, 17, 73, 39, 20

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OFFSET

1,2

COMMENTS

A divisor of n other than 1 or n is called nontrivial.

LINKS

Ridouane Oudra, Table of n, a(n) for n = 1..10000

FORMULA

a(n) = A063655(n) - A010051(n), for n>1. - Ridouane Oudra, May 24 2025

EXAMPLE

There are two ways to write 12 as a product of two nontrivial divisors, i.e., 6*2 and 4*3. Since 8=6+2>4+3=7, we have a(12)=7.

MAPLE

with(numtheory): a:=proc(n) if n=1 then 1; elif isprime(n)=true then n; else min(seq(d+n/d, d in divisors(n) minus{1, n})); fi; end: seq(a(n), n=1..100); # Ridouane Oudra, May 24 2025

MATHEMATICA

Table[If[Length[Divisors[n]] > 2, Min[Table[Divisors[n][[j]] + n/Divisors[n][[j]], {j, 2, Length[Divisors[n]] - 1}]], n], {n, 1, 100}] (* Stefan Steinerberger, Feb 04 2008 *)

PROG

(PARI) a(n) = {my(d = divisors(n)); if(#d > 2, d[ceil((#d+1)/2)] + d[ceil((#d)/2)], n)} \\ David A. Corneth, May 24 2025

CROSSREFS

Cf. A063655, A010051.

Sequence in context: A262049 A337310 A001414 * A134889 A303702 A319057

Adjacent sequences: A134872 A134873 A134874 * A134876 A134877 A134878

KEYWORD

nonn,easy

AUTHOR

Joseph L. Pe, Feb 01 2008

EXTENSIONS

More terms from Stefan Steinerberger, Feb 04 2008

STATUS

approved