|
Search: id:A066760
|
|
|
| A066760 |
|
Sum_{1<=k<=n, k is not a divisor of n, and k is not coprime to n} k. |
|
+0
3
|
|
| 0, 0, 0, 0, 0, 4, 0, 6, 6, 18, 0, 27, 0, 40, 37, 42, 0, 79, 0, 89, 74, 108, 0, 145, 45, 154, 96, 183, 0, 274, 0, 210, 184, 270, 163, 360, 0, 340, 257, 411, 0, 556, 0, 467, 418, 504, 0, 669, 140, 683, 439, 657, 0, 880, 369, 805, 548, 810, 0, 1183, 0, 928, 779, 930, 502
(list; graph; listen)
|
|
|
OFFSET
|
0,6
|
|
|
COMMENT
|
This function can be used to prove no p^k is perfect or multi-perfect (see Epsilon and Delta)
|
|
LINKS
|
Jon Perry, Epsilon and Delta
|
|
FORMULA
|
a(n) = 1+n*(n+1)/2-sigma(n)-n*phi(n)/2
a(n)=0 iff n=1, 4 or a prime. (Robert G. Wilson v, Jul 31 2004)
|
|
EXAMPLE
|
There are 3 integers that satisfy this definition for n=12, namely 8, 9 and 10. These sum to 27, hence a(12)=27
|
|
MATHEMATICA
|
Table[n(n + 1)/2 + 1 - EulerPhi[n]*n/2 - DivisorSigma[1, n], {n, 2, 65}] (RWGv)
|
|
PROGRAM
|
(PARI) for (n=1, 100, write1("epsilon.txt", 1+n*(n+1)/2-sigma(n)-n*eulerphi(n)/2, ", "))
|
|
CROSSREFS
|
Cf. A000010, A000203, A000217, A023896, A024816, A045763.
Sequence in context: A133995 A019629 A073759 this_sequence A102393 A019833 A027857
Adjacent sequences: A066757 A066758 A066759 this_sequence A066761 A066762 A066763
|
|
KEYWORD
|
nonn
|
|
AUTHOR
|
Jon Perry (perry(AT)globalnet.co.uk), Jan 17 2002
|
|
|
Search completed in 0.002 seconds
|
