|
Search: id:A064193
|
|
|
| A064193 |
|
Product of divisors of n and sum of unitary divisors of n are both perfect squares. |
|
+0
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; listen)
|
|
|
OFFSET
|
1,2
|
|
|
LINKS
|
Harry J. Smith, Table of n, a(n) for n=1,...,1000
|
|
PROGRAM
|
(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)) ) } [From Harry J. Smith (hjsmithh(AT)sbcglobal.net), Sep 23 2009]
|
|
CROSSREFS
|
Cf. A034448, A007955.
Sequence in context: A060390 A019281 A013630 this_sequence A063301 A030999 A113744
Adjacent sequences: A064190 A064191 A064192 this_sequence A064194 A064195 A064196
|
|
KEYWORD
|
easy,nonn
|
|
AUTHOR
|
Jason Earls (zevi_35711(AT)yahoo.com), Oct 14 2001
|
|
EXTENSIONS
|
Erroneous PARI program of Sep 09 2009 deleted by Harry J. Smith (hjsmithh(AT)sbcglobal.net), Sep 23 2009
|
|
|
Search completed in 0.002 seconds
|
