|
|
A124876
|
|
Number of prime factors (counted with multiplicity) in factorization of A007408(n).
|
|
3
|
|
|
0, 2, 1, 3, 2, 4, 3, 2, 3, 5, 3, 3, 3, 2, 1, 4, 2, 5, 1, 3, 2, 6, 2, 4, 2, 1, 3, 5, 3, 6, 1, 2, 3, 2, 3, 10, 4, 4, 5, 5, 8, 7, 7, 2, 4, 7, 3, 2, 4, 3, 2, 5, 3, 4, 2, 8, 3, 4, 4, 5, 3, 3, 7, 2, 5, 10, 4, 2, 6, 8, 3, 6, 6, 4, 3, 6, 4, 7, 4, 4, 3, 4, 8, 5, 7, 4
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
OFFSET
|
1,2
|
|
LINKS
|
|
|
FORMULA
|
|
|
EXAMPLE
|
a(1) = 0 since A007408(1) = 1 contains no prime factor,
a(2) = 2 since A007408(2) = 9 = 3 * 3,
a(3) = 1 since A007408(3) = 251 is prime,
a(6) = 4 since A007408(6) = 7 * 7 * 11 * 53.
|
|
MAPLE
|
seq( add(op(2, j), j=op(2, (ifactors@A007408)(n))), n=1..28 );
A001222 := proc(n) numtheory[bigomega](n) ; end: b := fscanf("b007408.txt", "%d %d") : while b <> [] do printf("%d, ", A001222(op(2, b))) ; b := fscanf("b007408.txt", "%d %d") : od : # R. J. Mathar, May 18 2007
|
|
MATHEMATICA
|
Table[PrimeOmega[Numerator[Sum[1/k^3, {k, 1, n}]]], {n, 1, 50}] (* Amiram Eldar, Feb 09 2020 *)
PrimeOmega[Numerator[Accumulate[1/Range[50]^3]]] (* Harvey P. Dale, Aug 28 2023 *)
|
|
CROSSREFS
|
|
|
KEYWORD
|
nonn
|
|
AUTHOR
|
|
|
EXTENSIONS
|
|
|
STATUS
|
approved
|
|
|
|