|
|
A253141
|
|
If n is a prime power, then a(n) = lambda(tau(n)) = A014963(A000005(n)); otherwise, a(n) = 1.
|
|
2
|
|
|
1, 2, 2, 3, 2, 1, 2, 2, 3, 1, 2, 1, 2, 1, 1, 5, 2, 1, 2, 1, 1, 1, 2, 1, 3, 1, 2, 1, 2, 1, 2, 1, 1, 1, 1, 1, 2, 1, 1, 1, 2, 1, 2, 1, 1, 1, 2, 1, 3, 1, 1, 1, 2, 1, 1, 1, 1, 1, 2, 1, 2, 1, 1, 7, 1, 1, 2, 1, 1, 1, 2, 1, 2, 1, 1, 1, 1, 1, 2, 1, 5, 1, 2, 1, 1, 1, 1
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
OFFSET
|
1,2
|
|
COMMENTS
|
For any integer sequence a, the sequence b such that b(n) = Product_{d|n} a(d) is a divisibility sequence. Since A253139(n) = Product_{d|n} a(d), A253139 is a divisibility sequence.
a(n) depends only on prime signature of n (cf. A025487). So a(24) = a(375) since 24 = 2^3*3 and 375 = 3*5^3 both have prime signature (3,1).
|
|
LINKS
|
|
|
EXAMPLE
|
2 is a prime number, i.e., a prime power with 2 divisors; a(2) = A014963(2) = 2.
6 = 2*3 is not a prime power; a(6) = 1.
8 = 2^3 is a prime power with 4 divisors; a(8) = A014963(4) = 2.
32 = 2^5 is a prime power with 6 divisors; a(32) = A014963(6) = 1.
|
|
MATHEMATICA
|
Table[If[PrimePowerQ[n], Exp[MangoldtLambda[DivisorSigma[0, n]]], 1], {n, 1, 100}] (* Indranil Ghosh, Jul 19 2017 *)
|
|
PROG
|
(PARI)
|
|
CROSSREFS
|
|
|
KEYWORD
|
nonn,easy
|
|
AUTHOR
|
|
|
STATUS
|
approved
|
|
|
|