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A071575
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Number of iterations of cototient(n) needed to reach 1 (cototient(n) = n-phi(n)).
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2
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0, 1, 1, 2, 1, 3, 1, 3, 2, 4, 1, 4, 1, 4, 2, 4, 1, 5, 1, 5, 3, 5, 1, 5, 2, 5, 3, 5, 1, 6, 1, 5, 2, 6, 2, 6, 1, 6, 3, 6, 1, 7, 1, 6, 4, 6, 1, 6, 2, 7, 2, 6, 1, 7, 3, 6, 4, 7, 1, 7, 1, 6, 4, 6, 2, 7, 1, 7, 3, 7, 1, 7, 1, 7, 3, 7, 2, 8, 1, 7, 4, 8, 1, 8, 4, 7, 2, 7, 1, 8, 2, 7, 3, 7, 2, 7, 1, 7, 4, 8, 1, 8, 1, 7, 5, 8
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OFFSET
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1,4
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LINKS
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FORMULA
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a(n) = a(n-phi(n))+1, a(1) = 0.
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EXAMPLE
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cototient(6) = 4, cototient(4) = 2, cototient(2) = 1, hence a(6) = 3.
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MATHEMATICA
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cot[n_] := n - EulerPhi[n]; a[n_] := -1 + Length @ NestWhileList[cot, n, # > 1 &]; Array[a, 100] (* Amiram Eldar, May 19 2022 *)
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PROG
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(PARI) for(n=1, 150, s=n; t=0; while(s!=1, t++; s=s-eulerphi(s); if(s==1, print1(t, ", "); ); ))
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CROSSREFS
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KEYWORD
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easy,nonn
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AUTHOR
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EXTENSIONS
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Prepended a(1)=0 and changed offset. - T. D. Noe, Dec 03 2008
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STATUS
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approved
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