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Search: id:A053036
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| A053036 |
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Number of values which are not powers of 2 in the trajectory when A051593 (cototient function) is repeatedly applied starting with n!. |
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2
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| 1, 1, 2, 2, 4, 5, 7, 7, 9, 20, 22, 23, 35, 38, 35, 35, 48, 54, 62, 79, 79, 85, 64, 65, 108, 124, 133, 130, 120, 158, 128, 128, 170, 181, 179, 189, 220, 181, 226, 228, 192, 255, 268, 268, 269, 292, 291, 286, 317, 324, 337, 288, 354, 352, 384, 378, 396, 345, 426, 393
(list; graph; listen)
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OFFSET
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1,3
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COMMENT
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Unlike the analogous sequence based on A000005, the non-powers 2 which emerge during iteration are initial, consecutive iterates, except the last one=0.
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EXAMPLE
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n=9, initial value=9!=362880, the successive iterates when the cototient function (A051953) is repeatedly applied are: {362880,279936,186624,124416,82944,55296,36864,24576, 16384,8192,4096,2048,1024,512,256,128,64,32,16,8,4,2,1,0} This includes 8 initial and 1 terminal(it is the 0) which are not powers of 2. So a(9)=8+1=9. Beside 15 2-powers appear.
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PROGRAM
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(PARI) cototient(x)= x - eulerphi(x) FunctionIterate(f, x, t)= {local(retval); retval = vector(0); while(x!=t, x = eval(concat(f, "(x)")); retval = concat(retval, x)); retval; } A053036(x) = {local(li, fa, count); count = 0; li = concat([x! ], FunctionIterate("cototient", x!, 0)); for(i=1, #li, fa = factor(li[i]); if(((matsize(fa)[1] == 1) && (fa[1, 1] == 2)) || (matsize(fa)[1] == 0), 0, count++)); count} for(i=1, 64, print1(A053036(i), ", ")) - Olaf Voss (richyfourtythree(AT)yahoo.com), Feb 20 2008
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CROSSREFS
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Cf. A051593, A053475.
Sequence in context: A085140 A138883 A107849 this_sequence A067957 A120326 A036406
Adjacent sequences: A053033 A053034 A053035 this_sequence A053037 A053038 A053039
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KEYWORD
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nonn
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AUTHOR
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Labos E. (labos(AT)ana.sote.hu), Feb 24 2000
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EXTENSIONS
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More terms from Olaf Voss (richyfourtythree(AT)yahoo.com), Feb 20 2008
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