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A065371 a(1) = 1, a(prime(i)) = prime(i) - i for i > 0 and a(u * v) = a(u) * a(v) for u, v > 0. 4
1, 1, 1, 1, 2, 1, 3, 1, 1, 2, 6, 1, 7, 3, 2, 1, 10, 1, 11, 2, 3, 6, 14, 1, 4, 7, 1, 3, 19, 2, 20, 1, 6, 10, 6, 1, 25, 11, 7, 2, 28, 3, 29, 6, 2, 14, 32, 1, 9, 4, 10, 7, 37, 1, 12, 3, 11, 19, 42, 2, 43, 20, 3, 1, 14, 6, 48, 10, 14, 6, 51, 1, 52, 25, 4, 11, 18, 7, 57, 2, 1, 28, 60, 3, 20, 29 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,5

COMMENTS

a(n) > 0 and a(n) < n for all n > 1.

LINKS

Reinhard Zumkeller, Table of n, a(n) for n = 1..10000

FORMULA

a(1) = 1; for n > 1, a(n) = (A020639(n)-A055396(n)) * a(A032742(n)). - Antti Karttunen, Jan 12 2017

EXAMPLE

a(210) = a(2*3*5*7) = a(2)*a(3)*a(5)*a(7) = (prime(1)-1)*(prime(2)-2)*(prime(3)-3)*(prime(4)-4) = (2-1)*(3-2)*(5-3)*(7-4) = 1*1*2*3 = 6.

PROG

(Haskell)

a065371 1 = 1

a065371 n = product $ map (a014689 . a049084) $ a027746_row n

-- Reinhard Zumkeller, Apr 09 2012

(Scheme, with memoization-macro definec)

(definec (A065371 n) (cond ((= 1 n) 1) (else (* (- (A020639 n) (A055396 n)) (A065371 (A032742 n))))))

;; Antti Karttunen, Jan 12 2017

CROSSREFS

Cf. A000040, A014689, A020639, A027746, A032742, A049084, A055396, A065372, A065373, A065374.

Sequence in context: A117811 A297381 A051793 * A300982 A186007 A212623

Adjacent sequences:  A065368 A065369 A065370 * A065372 A065373 A065374

KEYWORD

mult,nonn

AUTHOR

Reinhard Zumkeller, Nov 01 2001

STATUS

approved

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Last modified April 24 12:01 EDT 2019. Contains 322429 sequences. (Running on oeis4.)