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A063937 Sum of unitary divisors of n is a square > 1. 3
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 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

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

LINKS

Harry J. Smith, Table of n, a(n) for n = 1..1000

FORMULA

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

EXAMPLE

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

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 http://mathworld.wolfram.com/UnitaryDivisor.html *)

PROG

(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

(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

CROSSREFS

Cf. A034448, A063936.

Sequence in context: A148769 A156291 A111136 * A178525 A266187 A202192

Adjacent sequences:  A063934 A063935 A063936 * A063938 A063939 A063940

KEYWORD

easy,nice,nonn

AUTHOR

Felice Russo, Aug 31 2001

STATUS

approved

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Last modified December 12 23:01 EST 2018. Contains 318081 sequences. (Running on oeis4.)