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 A064193 Numbers whose product of divisors and sum of unitary divisors are both squares. 1
 1, 8, 22, 24, 66, 70, 94, 115, 119, 170, 210, 214, 217, 228, 265, 282, 310, 322, 345, 357, 382, 385, 490, 497, 510, 517, 522, 527, 580, 642, 651, 679, 710, 742, 745, 782, 795, 862, 889, 920, 930, 935, 948, 952, 966, 970, 1066, 1146, 1155, 1174, 1177, 1197 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 LINKS Harry J. Smith, Table of n, a(n) for n = 1..1000 PROG (PARI) a(n) = n^(numdiv(n)/2); {usigma(n, s=1, fac, i) = fac=factor(n); for(i=1, matsize(fac)[1], s=s*(1+fac[i, 1]^fac[i, 2]) ); return(s); } for(n=1, 3000, if(issquare(a(n)) && issquare(usigma(n)), print1(n, ", "))) (PARI) pd(n)= { d=numdiv(n); if (d%2, round(sqrt(n))^d, n^(d/2)) } usigma(n)= { local(f, s=1); f=factor(n); for(i=1, matsize(f)[1], s*=1 + f[i, 1]^f[i, 2]); return(s) } { n=0; for (m=1, 10^9, if (issquare(pd(m)) && issquare(usigma(m)), write("b064193.txt", n++, " ", m); if (n==1000, break)) ) } \\ Harry J. Smith, Sep 23 2009 CROSSREFS Cf. A034448, A007955. Sequence in context: A215600 A304301 A236917 * A301482 A213017 A305515 Adjacent sequences:  A064190 A064191 A064192 * A064194 A064195 A064196 KEYWORD easy,nonn AUTHOR Jason Earls, Oct 14 2001 EXTENSIONS Erroneous PARI program of Sep 09 2009 deleted by Harry J. Smith, Sep 23 2009 STATUS approved

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Last modified August 11 15:10 EDT 2022. Contains 356066 sequences. (Running on oeis4.)