A063937 Sum of unitary divisors of n is a square > 1.

3, 8, 22, 24, 66, 70, 76, 94, 115, 119, 170, 210, 214, 217, 228, 252, 265, 282, 310, 316, 322, 345, 357, 382, 385, 490, 497, 510, 517, 522, 527, 580, 612, 642, 651, 679, 710, 716, 742, 745, 782, 795, 801, 833, 862, 889, 920, 930, 935, 948, 952, 966, 970

Offset: 1

Author

Felice Russo, Aug 31 2001

Keywords

• easy
• nice
• nonn

Comments

A unitary divisor of n is a divisor d of n such that gcd(d, n/d) = 1.

Examples

			The unitary divisors of 3 are 1,3 and then 3 + 1 = 4 is a square.
		

Links

• Amiram Eldar, Table of n, a(n) for n = 1..10000 (terms 1..1000 from Harry J. Smith)

Crossrefs

Cf. A034448, A063936.

Programs

Haskell

import Data.List (findIndices)
a063937 n = a063937_list !! (n-1)
a063937_list = map (+ 2) $
               findIndices ((== 1) . a010052) $ tail a034448_list
-- Reinhard Zumkeller, Aug 15 2012

Mathematica

udQ[n_]:=Module[{totdivs=Total[Sort[Flatten[Outer[Times,Sequence@@({1,#}&/@Power@@@FactorInteger[n])]]]]},totdivs>1&&IntegerQ[Sqrt[totdivs]]]; Select[Range[1000],udQ] (* Harvey P. Dale, Apr 22 2012, using program from Eric Weisstein at https://mathworld.wolfram.com/UnitaryDivisor.html *)

PARI

us(n) = sumdiv(n, d, if(gcd(d, n/d)==1, d))
{ n=0; for (m=1, 10^9, u=us(m); if (issquare(u) && u > 1, write("b063937.txt", n++, " ", m); if (n==1000, break)) ) } \\ Harry J. Smith, Sep 03 2009

Formula

a(n) > 1 and A010052(A034448(a(n))) = 1. - Reinhard Zumkeller, Aug 15 2012