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A112624 If p^b(p,n) is the highest power of the prime p dividing n, then a(n) = product_{p|n} b(p,n)!. 5
1, 1, 1, 2, 1, 1, 1, 6, 2, 1, 1, 2, 1, 1, 1, 24, 1, 2, 1, 2, 1, 1, 1, 6, 2, 1, 6, 2, 1, 1, 1, 120, 1, 1, 1, 4, 1, 1, 1, 6, 1, 1, 1, 2, 2, 1, 1, 24, 2, 2, 1, 2, 1, 6, 1, 6, 1, 1, 1, 2, 1, 1, 2, 720, 1, 1, 1, 2, 1, 1, 1, 12, 1, 1, 2, 2, 1, 1, 1, 24, 24, 1, 1, 2, 1, 1, 1, 6, 1, 2, 1, 2, 1, 1, 1, 120, 1, 2, 2, 4, 1 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,4

COMMENTS

The logarithm of the Dirichlet series with the reciprocals of this sequence as coefficients, is the Dirichlet series with the characteristic function of primes A010051 as coefficients.

LINKS

Antti Karttunen, Table of n, a(n) for n = 1..10000

Index entries for sequences computed from exponents in factorization of n

FORMULA

From Antti Karttunen, May 29 2017: (Start)

a(1) = 1 and for n > 1, a(n) = A000142(A067029(n)) * a(A028234(n)).

a(n) = A246660(A156552(n)). (End)

EXAMPLE

45 = 3^2 * 5^1. So a(45) = 2! * 1! = 2.

MAPLE

w := proc (n) options operator, arrow: op(2, ifactors(n)) end proc: a := proc (n) options operator, arrow: mul(factorial(w(n)[j][2]), j = 1 .. nops(w(n))) end proc: seq(a(n), n = 1 .. 101); # Emeric Deutsch, May 17 2012

MATHEMATICA

f[n_] := Block[{fi = Last@Transpose@FactorInteger@n}, Times @@ (fi!)]; Array[f, 101] (* Robert G. Wilson v, Dec 27 2005 *)

PROG

(PARI) A112624(n) = { my(f = factor(n), m = 1); for (k=1, #f~, m *= f[k, 2]!; ); m; } \\ Antti Karttunen, May 28 2017

(Sage)

def A112624(n):

    return mul(factorial(i) for i in [s[1] for s in list(factor(n))])

[A112624(i) for i in (1..101)]  # Peter Luschny, Jun 15 2013

(Scheme) (define (A112624 n) (if (= 1 n) n (* (A000142 (A067029 n)) (A112624 (A028234 n))))) ;; Antti Karttunen, May 29 2017

CROSSREFS

For row > 1: a(n) = row products of A100995(A126988), when neglecting zero elements.

Cf. A000142, A028234, A067029, A112622, A112623, A156552, A246660.

Sequence in context: A060185 A129110 A257101 * A294875 A293902 A300830

Adjacent sequences:  A112621 A112622 A112623 * A112625 A112626 A112627

KEYWORD

nonn,mult

AUTHOR

Leroy Quet, Dec 25 2005

EXTENSIONS

More terms from Robert G. Wilson v, Dec 27 2005

STATUS

approved

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Last modified August 17 17:05 EDT 2018. Contains 313816 sequences. (Running on oeis4.)