A072866 Smallest k > 1 dividing tau(k*2^n) (cf. A000005).

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

Offset

0,1

Comments

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).

Links

Antti Karttunen, Table of n, a(n) for n = 0..16384

Prog

(PARI) A072866(n) = { n = (1<<n); for(k=2, oo, if(!(numdiv(k*n)%k), return(k))); }; \\ Antti Karttunen, Feb 06 2019

Crossrefs

Cf. A000005.

Sequence in context: A188813 A324958 A353108 * A061393 A260361 A055935

Adjacent sequences: A072863 A072864 A072865 * A072867 A072868 A072869

Keyword

easy,nonn

Author

Benoit Cloitre, Jul 27 2002

Status

approved