A290106 a(1) = 1; for n > 1, if n = Product prime(k)^e(k), then a(n) = Product (k)^(e(k)-1).

1, 1, 1, 1, 1, 1, 1, 1, 2, 1, 1, 1, 1, 1, 1, 1, 1, 2, 1, 1, 1, 1, 1, 1, 3, 1, 4, 1, 1, 1, 1, 1, 1, 1, 1, 2, 1, 1, 1, 1, 1, 1, 1, 1, 2, 1, 1, 1, 4, 3, 1, 1, 1, 4, 1, 1, 1, 1, 1, 1, 1, 1, 2, 1, 1, 1, 1, 1, 1, 1, 1, 2, 1, 1, 3, 1, 1, 1, 1, 1, 8, 1, 1, 1, 1, 1, 1, 1, 1, 2, 1, 1, 1, 1, 1, 1, 1, 4, 2, 3, 1, 1, 1, 1, 1, 1, 1, 4, 1, 1, 1, 1, 1, 1, 1, 1, 2, 1, 1, 1

Offset: 1

Author

Antti Karttunen, Aug 13 2017

Keywords

• nonn
• mult

Examples

			For n = 21 = 3*7 = prime(2)^1 * prime(4)^1, a(n) = 2^0 * 4^0 = 1*1 = 1.
For n = 360 = 2^3 * 3^2 * 5^1 = prime(1)^3 * prime(2)^2 * prime(3)^1, a(n) = 1^2 * 2^1 * 3^0 = 1*2*1 = 2.
		

Links

• Antti Karttunen, Table of n, a(n) for n = 1..10000
• Index entries for sequences computed from indices in prime factorization

Crossrefs

Cf. A003557, A003963, A007947, A156061, A290105.

Differs from A290104 for the first time at n=21.

Programs

Mathematica

Table[If[n == 1, 1, Apply[Times, Map[PrimePi[#1]^#2 & @@ # &, #]] / Apply[Times, PrimePi[#[[All, 1]] ]]] &@ FactorInteger@ n, {n, 120}] (* Michael De Vlieger, Aug 14 2017 *)

Scheme

(define (A290106 n) (/ (A003963 n) (A156061 n)))
(define (A290106 n) (if (= 1 n) 1 (* (expt (A055396 n) (- (A067029 n) 1)) (A290106 (A028234 n)))))

Formula

Multiplicative with a(prime(k)^e) = k^(e-1).

a(n) = A003963(n) / A156061(n).

a(n) = A003963(A003557(n)) = A003963(n/A007947(n)).