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A173557 a(n) = Product_{p-1 | p is prime and divisor of n}. 39
1, 1, 2, 1, 4, 2, 6, 1, 2, 4, 10, 2, 12, 6, 8, 1, 16, 2, 18, 4, 12, 10, 22, 2, 4, 12, 2, 6, 28, 8, 30, 1, 20, 16, 24, 2, 36, 18, 24, 4, 40, 12, 42, 10, 8, 22, 46, 2, 6, 4, 32, 12, 52, 2, 40, 6, 36, 28, 58, 8, 60, 30, 12, 1, 48, 20, 66, 16, 44, 24, 70, 2, 72, 36 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,3

COMMENTS

This is A023900 without the signs. - T. D. Noe, Jul 31 2013

a(A056867(n)) = 1. - Reinhard Zumkeller, Jun 01 2015

LINKS

Alois P. Heinz, Table of n, a(n) for n = 1..65536 (first 1000 terms from T. D. Noe)

FORMULA

a(n) = A003958(n) iff n is squarefree. a(n)= |A023900(n)|.

Multiplicative with a(p^e) = p-1, e>=1. - R. J. Mathar, Mar 30 2011

a(n) = phi(rad(n)) = A000010(A007947(n)). - Enrique Pérez Herrero, May 30 2012

a(n) = A000010(n) / A003557(n). - Jason Kimberley, Dec 09 2012

Dirichlet g.f.: zeta(s) * Product_{p prime} (1 - 2p^(-s) + p^(1-s)). The Dirichlet inverse is multiplicative with b(p^e) = (1 - p) * (2 - p)^(e - 1) = Sum_k A118800(e, k) * p^k. - Álvar Ibeas, Nov 24 2017

a(1) = 1; for n > 1, a(n) = (A020639(n)-1) * a(A028234(n)). - Antti Karttunen, Nov 28 2017

EXAMPLE

300 = 3*5^2*2^2 => a(300) = (3-1)*(2-1)*(5-1) = 8.

MAPLE

A173557 := proc(n) local dvs; dvs := numtheory[factorset](n) ; mul(d-1, d=dvs) ; end proc: # R. J. Mathar, Feb 02 2011

# second Maple program:

a:= n-> mul(i[1]-1, i=ifactors(n)[2]):

seq(a(n), n=1..80);  # Alois P. Heinz, Aug 27 2018

MATHEMATICA

a[n_] := Module[{fac = FactorInteger[n]}, If[n==1, 1, Product[fac[[i, 1]]-1, {i, Length[fac]}]]]; Table[a[n], {n, 100}]

PROG

(Haskell)

a173557 1 = 1

a173557 n = product $ map (subtract 1) $ a027748_row n

-- Reinhard Zumkeller, Jun 01 2015

(PARI) a(n) = my(f=factor(n)[, 1]); prod(k=1, #f, f[k]-1); \\ Michel Marcus, Oct 31 2017

(Scheme, with memoization-macro definec) (definec (A173557 n) (if (= 1 n) 1 (* (- (A020639 n) 1) (A173557 (A028234 n))))) ;; Antti Karttunen, Nov 28 2017

CROSSREFS

Cf. A023900, A141564.

Cf. A027748, A056867.

Sequence in context: A300234 A070777 A173614 * A023900 A141564 A239641

Adjacent sequences:  A173554 A173555 A173556 * A173558 A173559 A173560

KEYWORD

nonn,easy,mult

AUTHOR

José María Grau Ribas, Feb 21 2010

STATUS

approved

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Last modified November 21 13:45 EST 2018. Contains 317449 sequences. (Running on oeis4.)