|
Search: id:A091732
|
|
|
| A091732 |
|
Iphi(n): infinitary analogue of Euler's phi function. |
|
+0
2
|
|
| 1, 1, 2, 3, 4, 2, 6, 3, 8, 4, 10, 6, 12, 6, 8, 15, 16, 8, 18, 12, 12, 10, 22, 6, 24, 12, 16, 18, 28, 8, 30, 15, 20, 16, 24, 24, 36, 18, 24, 12, 40, 12, 42, 30, 32, 22, 46, 30, 48, 24, 32, 36, 52, 16, 40, 18, 36, 28, 58, 24, 60, 30, 48, 45, 48, 20, 66, 48, 44, 24, 70, 24, 72, 36, 48
(list; graph; listen)
|
|
|
OFFSET
|
1,3
|
|
|
COMMENT
|
Not the same as A064380.
|
|
REFERENCES
|
G. L. Cohen and P. Hagis, Arithmetic functions associated with the infinitary divisors of an integer, Internat. J. Math. Math. Sci. 16 (1993) 373-383.
|
|
LINKS
|
S. R. Finch, Unitarism and infinitarism.
|
|
FORMULA
|
Consider the set, I, of integers of the form p^(2^j), where p is any prime and j >= 0. Let n > 1. From the fundamental theorem of arithmetic and the fact that the binary representation of any integer is unique, it follows that n can be uniquely factored as a product of distinct elements of I. If n = P_1*P_2*...*P_t, where each P_j is in I, then iphi(n) = prod (P_j - 1), where j runs from 1 to t.
|
|
EXAMPLE
|
a(6)=2 since 6=P_1*P_2, where P_1=2^(2^0) and P_2=3^(2^0); hence (P_1-1)*(P_2-1)=2.
|
|
CROSSREFS
|
Cf. A037445, A049417, A050376.
Sequence in context: A026346 A120636 A117744 this_sequence A109746 A061020 A047994
Adjacent sequences: A091729 A091730 A091731 this_sequence A091733 A091734 A091735
|
|
KEYWORD
|
nonn
|
|
AUTHOR
|
S. R. Finch (Steven.Finch(AT)inria.fr), Mar 05 2004
|
|
|
Search completed in 0.002 seconds
|
