|
Search: id:A063829
|
|
|
| A063829 |
|
usigma(n)=2n + d(n), where d(n) is the number of divisors of n. |
|
+0
1
|
|
| 150, 294, 726, 1014, 1428, 1734, 2166, 3174, 5046, 5766, 8214, 10086, 11094, 13254, 16854, 20886, 22326, 26934, 30246, 31974, 37446, 41334, 47526, 56454, 61206, 63654, 68694, 71286, 76614, 96774, 102966, 112614, 115926, 133206, 136806
(list; graph; listen)
|
|
|
OFFSET
|
1,1
|
|
|
COMMENT
|
"The sequence includes all numbers of the form 6 * p^2 with p a prime >= 5. All of the terms above are of this form, except for 1428. There are similar subsequences corresponding to each of the five known unitary perfect numbers (A002827), namely 60 * p^9 (p>=7), 90 * p^14 (p>=7), 87360 * p^1559 (p=11 or p>=17), and 146361946186458562560000 * p^3009086064688703999 (p>=17 and not equal to 19, 37, 79, 109, 157, or 313). It is not known if there are other terms in the sequence besides these and 1428." - Dean Hickerson. (The term 33872160 was found later: it is not of the form a * p^e where a is a unitary perfect number and p is a prime not dividing a. -JE )
|
|
PROGRAM
|
(PARI) us(n)=sumdiv(n, d, if(gcd(d, n/d)==1, d)); for(n=1, 10^8, if(us(n)==2*n+numdiv(n), print(n)))
|
|
CROSSREFS
|
Cf. A002827.
Sequence in context: A054729 A116185 A008889 this_sequence A140671 A054558 A073614
Adjacent sequences: A063826 A063827 A063828 this_sequence A063830 A063831 A063832
|
|
KEYWORD
|
nice,nonn
|
|
AUTHOR
|
Jason Earls (zevi_35711(AT)yahoo.com), Aug 20 2001
|
|
|
Search completed in 0.002 seconds
|
