|
|
A308317
|
|
Multiplicative with a(prime(k)^e) = A005117(e+1)^(2^(k-1)).
|
|
1
|
|
|
1, 2, 4, 3, 16, 8, 256, 5, 9, 32, 65536, 12, 4294967296, 512, 64, 6, 18446744073709551616, 18, 340282366920938463463374607431768211456, 48, 1024, 131072, 115792089237316195423570985008687907853269984665640564039457584007913129639936, 20, 81, 8589934592, 25
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
OFFSET
|
1,2
|
|
COMMENTS
|
This sequence is a permutation of the natural numbers (with inverse A308328).
The property of being a bijection is easily deduced from the Fermi-Dirac representation of a number.
The first known fixed points are: 1, 2, 9, 12, 18, 3584, 32256.
|
|
LINKS
|
|
|
FORMULA
|
a(2^e) = A005117(e+1) for any e >= 0.
a(prime(k)) = A001146(k-1) for any k > 0.
|
|
EXAMPLE
|
a(3) = a(prime(2)) = A001146(1) = 2^(2^1) = 4.
a(96) = a(2^5 * 3) = a(2^5) * a(3) = 7 * 4 = 28.
|
|
PROG
|
(PARI) A005117(n) = for (k=1, oo, if (issquarefree(k), if (n--==0, return (k))))
a(n) = my (f=factor(n)); prod (i=1, #f~, A005117(1+f[i, 2])^(2^(primepi(f[i, 1])-1)))
|
|
CROSSREFS
|
|
|
KEYWORD
|
nonn,mult
|
|
AUTHOR
|
|
|
STATUS
|
approved
|
|
|
|