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A072866
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Smallest k > 1 dividing tau(k*2^n) (cf. A000005).
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1
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2, 4, 2, 10, 2, 3, 2, 6, 2, 4, 2, 3, 2, 4, 2, 12, 2, 3, 2, 5, 2, 4, 2, 3, 2, 4, 2, 7, 2, 3, 2, 6, 2, 4, 2, 3, 2, 4, 2, 5, 2, 3, 2, 6, 2, 4, 2, 3, 2, 4, 2, 12, 2, 3, 2, 6, 2, 4, 2, 3, 2, 4, 2, 10, 2, 3, 2, 6, 2, 4, 2, 3, 2, 4, 2, 12, 2, 3, 2, 5, 2, 4, 2, 3, 2, 4, 2, 11, 2, 3, 2, 6, 2, 4, 2, 3, 2, 4, 2, 5, 2, 3
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OFFSET
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0,1
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COMMENTS
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Sequence contains the values 2,3,4,5,6,7,10,11,12 only. Is there any pattern ? a(m) = 4 for m =1,9,13,21,25,33,37,45,49,...This subsequence has the recurrence b(1)=1, b(2k)=b(2k-1)+8, b(2k+1)=b(2k)+4. If a(m) = 10 then m == 0 (mod 3). If m>n, a(n)=10, a(m)=10 then m-n == 0 (mod 60).
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LINKS
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PROG
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(PARI) A072866(n) = { n = (1<<n); for(k=2, oo, if(!(numdiv(k*n)%k), return(k))); }; \\ Antti Karttunen, Feb 06 2019
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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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STATUS
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approved
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