|
Search: id:A064116
|
|
|
| A064116 |
|
Sequence of composite numbers whose sum of aliquot divisors as well as product of aliquot divisors is a perfect square. |
|
+0
2
|
|
| 12, 75, 76, 124, 147, 153, 176, 243, 332, 363, 477, 507, 524, 575, 688, 867, 892, 963, 1075, 1083, 1421, 1532, 1573, 1587, 1611, 1916, 2032, 2075, 2224, 2299, 2401, 2421, 2523, 2572, 2883, 2891, 3100, 3479, 3776, 3888, 4107, 4336, 4527, 4961, 4975, 5043
(list; graph; listen)
|
|
|
OFFSET
|
1,1
|
|
|
LINKS
|
Harry J. Smith, Table of n, a(n) for n=1,...,1000
|
|
EXAMPLE
|
a(2)=75 because sum of aliquot divisors of 75 = 1+3+5+15+25=49=7^2 and product of aliquot divisors of 75 = 1*3*5*15*25 = 75^2
|
|
MATHEMATICA
|
Do[d = Delete[ Divisors[n], -1]; If[ !PrimeQ[n] && IntegerQ[ Sqrt[ Apply[ Plus, d]]] && IntegerQ[ Sqrt[ Apply[ Times, d]]], Print[n]], {n, 2, 10^4} ]
|
|
PROGRAM
|
(PARI) pad(n)= { local(d, p=1); d=divisors(n); for (i=1, length(d) - 1, p*=d[i]); return(p) } { n=0; for (m=2, 10^9, s=sigma(m) - m; if (s>1 && issquare(s) && issquare(pad(m)), write("b064116.txt", n++, " ", m); if (n==1000, break)) ) } [From Harry J. Smith (hjsmithh(AT)sbcglobal.net), Sep 07 2009]
|
|
CROSSREFS
|
Cf. A048699.
Sequence in context: A041270 A055912 A064121 this_sequence A003368 A092867 A053310
Adjacent sequences: A064113 A064114 A064115 this_sequence A064117 A064118 A064119
|
|
KEYWORD
|
base,easy,nonn
|
|
AUTHOR
|
Shyam Sunder Gupta (guptass(AT)rediffmail.com), Sep 09 2001
|
|
EXTENSIONS
|
More terms from Robert G. Wilson v (rgwv(AT)rgwv.com), Oct 05 2001
|
|
|
Search completed in 0.002 seconds
|
