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A053045
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EulerPhi is iterated with initial value n!; a(n) = number of powers of 2 among the iterates.
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3
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1, 2, 2, 4, 6, 7, 8, 11, 11, 14, 17, 19, 21, 23, 25, 29, 33, 34, 35, 39, 40, 44, 48, 51, 55, 58, 58, 61, 64, 67, 70, 75, 78, 83, 86, 88, 90, 92, 94, 99, 104, 106, 108, 113, 115, 120, 125, 129, 131, 136, 140, 144, 148, 149, 154, 158, 159, 163, 167, 171, 175, 179, 180
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OFFSET
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1,2
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COMMENTS
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Powers of 2 arise at the end of iterations without interruption. Analogous to A053035.
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LINKS
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FORMULA
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EXAMPLE
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For n=10, initial value = 3628800; the iteration chain is {3628800, 829440, 221184, 73728, 24576, 8192, 4096, 2048, 1024, 512, 256, 128, 64, 32, 16, 8, 4, 2, 1}. Its length is 19 and 14 values are powers of 2: 8192, ..., 1. Thus a(10)=14.
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MAPLE
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local a, e;
e := n! ;
a :=0 ;
while e > 1 do
if isA000079(e) then
a := a+1 ;
end if;
e := numtheory[phi](e) ;
end do:
1+a;
end proc:
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MATHEMATICA
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Table[Count[NestWhileList[EulerPhi, n!, # > 1 &], _?(IntegerQ@ Log2@ # &)], {n, 63}] (* Michael De Vlieger, Aug 15 2017 *)
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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