|
| |
|
|
A331596
|
|
Number of distinct prime factors of gcd(A122111(n), A241909(n)).
|
|
4
|
|
|
|
0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 1, 1, 2, 1, 1, 2, 1, 1, 1, 1, 1, 1, 1, 1, 2, 1, 1, 2, 1, 2, 1, 1, 1, 2, 1, 1, 2, 1, 1, 2, 1, 1, 1, 1, 2, 2, 1, 1, 1, 2, 1, 2, 1, 1, 1, 1, 1, 2, 1, 2, 2, 1, 1, 2, 2, 1, 1, 1, 1, 2, 1, 2, 2, 1, 1, 1, 1, 1, 1, 2, 1, 2, 1, 1, 1, 2, 1, 2, 1, 2, 1, 1, 2, 2, 1, 1, 2, 1, 1, 3
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
|
OFFSET
|
1,15
|
|
|
LINKS
|
Antti Karttunen, Table of n, a(n) for n = 1..65537
Index entries for sequences computed from indices in prime factorization
|
|
|
FORMULA
|
a(n) = A001221(A331596(n)) = A001221(gcd(A122111(n), A241909(n))).
a(n) = A001222(A331597(n)).
|
|
|
MATHEMATICA
|
Array[PrimeNu@ If[# == 1, 1, GCD @@ {Block[{k = #, m = 0}, Times @@ Power @@@ Table[k -= m; k = DeleteCases[k, 0]; {Prime@ Length@ k, m = Min@ k}, Length@ Union@ k]] &@ Catenate[ConstantArray[PrimePi[#1], #2] & @@@ #], Function[t, Times @@ Prime@ Accumulate[If[Length@ t < 2, {0}, Join[{1}, ConstantArray[0, Length@ t - 2], {-1}]] + ReplacePart[t, Map[#1 -> #2 & @@ # &, #]]]]@ ConstantArray[0, Transpose[#][[1, -1]]] &[# /. {p_, e_} /; p > 0 :> {PrimePi@ p, e}]} &@ FactorInteger[#]] &, 105] (* Michael De Vlieger, Jan 24 2020, after JungHwan Min at A122111. *)
|
|
|
PROG
|
(PARI) A331596(n) = omega(gcd(A122111(n), A241909(n)));
|
|
|
CROSSREFS
|
Cf. A001221, A331596, A335197.
Sequence in context: A101428 A307223 A321787 * A023586 A023584 A015182
Adjacent sequences: A331593 A331594 A331595 * A331597 A331598 A331599
|
|
|
KEYWORD
|
nonn
|
|
|
AUTHOR
|
Antti Karttunen, Jan 22 2020
|
|
|
STATUS
|
approved
|
| |
|
|
