|
| |
|
|
A182861
|
|
Number of distinct prime signatures represented among the unitary divisors of A025487(n).
|
|
3
|
|
|
|
1, 2, 2, 3, 2, 4, 2, 4, 4, 2, 3, 4, 6, 2, 4, 4, 6, 2, 4, 6, 4, 5, 3, 6, 2, 4, 8, 4, 8, 4, 6, 2, 4, 8, 4, 8, 4, 4, 6, 2, 6, 4, 9, 3, 8, 4, 8, 4, 6, 6, 2, 8, 4, 6, 12, 4, 8, 4, 8, 4, 6, 6, 2, 8, 4, 10, 12, 4, 6, 8, 4, 8, 6, 8, 4, 6, 9, 6, 3, 2, 8, 4, 10, 12, 4
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
|
OFFSET
|
1,2
|
|
|
COMMENTS
|
a(n) = number of members m of A025487 such that d(m^k) divides d(A025487(n)^k) for all values of k. (Here d(n) represents the number of divisors of n, or A000005(n).)
|
|
|
LINKS
|
Amiram Eldar, Table of n, a(n) for n = 1..10000
Eric Weisstein's World of Mathematics, Unitary Divisor
|
|
|
FORMULA
|
a(n) = A000005(A181820(n)).
If the canonical factorization of n into prime powers is Product p^e(p), then the formula for d(n^k) is Product_p (ek + 1). (See also A146289, A146290.)
|
|
|
EXAMPLE
|
60 has 8 unitary divisors (1, 3, 4, 5, 12, 15, 20 and 60). Primes 3 and 5 have the same prime signature, as do 12 (2^2*3) and 20 (2^2*5); each of the other four numbers listed is the only unitary divisor of 60 with its particular prime signature. Since a total of 6 distinct prime signatures appear among the unitary divisors of 60, and since 60 = A025487(13), a(13) = 6.
|
|
|
CROSSREFS
|
Cf. A000005, A025487, A034444, A085082, A146289, A146290, A181820, A182860, A182862.
Sequence in context: A218703 A326641 A144372 * A049238 A001616 A257599
Adjacent sequences: A182858 A182859 A182860 * A182862 A182863 A182864
|
|
|
KEYWORD
|
nonn
|
|
|
AUTHOR
|
Matthew Vandermast, Jan 14 2011
|
|
|
EXTENSIONS
|
More terms from Amiram Eldar, Jun 20 2019
|
|
|
STATUS
|
approved
|
| |
|
|
