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A064710 Sum of divisors of n and product of divisors of n are both perfect squares. 3
1, 22, 66, 70, 81, 94, 115, 119, 170, 210, 214, 217, 265, 282, 310, 322, 343, 345, 357, 364, 382, 385, 472, 497, 510, 517, 527, 642, 651, 679, 710, 742, 745, 782, 795, 820, 862, 884, 889, 930, 935, 966, 970, 1029, 1066, 1080, 1092, 1146, 1155, 1174 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

LINKS

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

MATHEMATICA

psQ[n_]:=Module[{d=Divisors[n]}, IntegerQ[Sqrt[Total[d]]] && IntegerQ[ Sqrt[Times@@d]]]; Select[Range[1200], psQ] (* Harvey P. Dale, Mar 07 2012 *)

PROG

(PARI) pd(n) = n^(numdiv(n)/2);

for(n=1, 2000, if(issquare(sigma(n)) && issquare(pd(n)), print1(n, ", ")))

(PARI) pd(n)= { d=numdiv(n); if (d%2, round(sqrt(n))^d, n^(d/2)) }

{ n=0; for (m=1, 10^9, if (issquare(sigma(m)) && issquare(pd(m)), write("b064710.txt", n++, " ", m); if (n==1000, break)) ) } \\ [Harry J. Smith, Sep 23 2009]

(Sage) [n for n in (1..100000) if sigma(n).is_square()and prod(divisors(n)).is_square()] # Giuseppe Coppoletta, Dec 16 2014

CROSSREFS

Cf. A007955, A000203.

Sequence in context: A124715 A126376 A136604 * A246415 A164136 A041946

Adjacent sequences:  A064707 A064708 A064709 * A064711 A064712 A064713

KEYWORD

easy,nonn

AUTHOR

Jason Earls, Oct 13 2001

EXTENSIONS

Corrected by Harvey P. Dale, Oct 23 2001

STATUS

approved

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Last modified June 16 06:46 EDT 2019. Contains 324145 sequences. (Running on oeis4.)