|
Search: id:A141807
|
|
|
| A141807 |
|
If p^b(n,p) is the largest power of the prime p to divide n, then the positive integer n is included in the sequence if p(1)^b(n,p(1)) = p(2)^b(n,p(2))+1 = p(3)^b(n,p(3))+2 =...= p(k)^b(n,p(k))+k-1, where (p(1),p(2),p(3),...,p(k)) is some permutation of the distinct primes that divide n. |
|
+0
2
|
|
| 1, 2, 3, 4, 5, 6, 7, 8, 9, 11, 12, 13, 16, 17, 19, 20, 23, 25, 27, 29, 31, 32, 37, 41, 43, 47, 49, 53, 56, 59, 60, 61, 64, 67, 71, 72, 73, 79, 81, 83, 89, 97, 101, 103, 107, 109, 113, 121, 125, 127, 128, 131, 137, 139, 149, 151, 157, 163, 167, 169, 173, 179, 181, 191
(list; graph; listen)
|
|
|
OFFSET
|
1,2
|
|
|
COMMENT
|
All prime-powers (A000961) are included in this sequence.
Sequence A141808 consists of terms of A141807 that are not prime powers.
|
|
LINKS
|
Leroy Quet, Home Page (listed in lieu of email address)
|
|
EXAMPLE
|
The prime-factorization of 60 is 2^2 *3^1 *5^1. Since 5^1 = 2^2 +1 = 3^1 +2 (ie, the prime powers, in some order, occur in an arithmetic progression with a difference of 1 between consecutive terms), then 60 is included in the sequence.
|
|
CROSSREFS
|
Cf. A141808.
Sequence in context: A055201 A072303 A081061 this_sequence A072495 A126968 A126969
Adjacent sequences: A141804 A141805 A141806 this_sequence A141808 A141809 A141810
|
|
KEYWORD
|
nonn
|
|
AUTHOR
|
Leroy Quet Jul 07 2008
|
|
EXTENSIONS
|
Extended by Ray Chandler (rayjchandler(AT)sbcglobal.net), Jun 21 2009
|
|
|
Search completed in 0.002 seconds
|
