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A190376
a(n) = sum (in ordinary arithmetic) of A067399(k), for k from 2^n to 2^(n+1)-1.
1
1, 4, 12, 31, 75, 175, 393, 864, 1868, 3978, 8394
OFFSET
0,2
COMMENTS
I was hoping this would turn out to be a known sequence, in which case we would learn something about the average values of A067399.
LINKS
D. Applegate, M. LeBrun and N. J. A. Sloane, Dismal Arithmetic [Note: we have now changed the name from "dismal arithmetic" to "lunar arithmetic" - the old name was too depressing]
MAPLE
read("transforms");
numbralADD := proc(a, b) option remember; ORnos(a, b) ; end proc:
numbralMUL := proc(a, b) option remember; local p, bshf, s ; p := 0 ; bshf := b ; for s from 0 do if bshf mod 2 <> 0 then p := numbralADD(p, 2^s*a ) ; end if; bshf := floor(bshf/2) ; if bshf = 0 then return p; end if; end do; end proc:
isnumbralDiv := proc(n, d) option remember; for e from 0 do if numbralMUL(e, d) = n then return true; elif numbralMUL(e, d) > 2*n then return false; end if; end do: end proc:
numbralDivisors := proc(n) option remember; local d, i; d := {} ; for i from 1 to n do if isnumbralDiv(n, i) then d := d union {i} ; end if; end do: d ; end proc:
A067399 := proc(n) nops(numbralDivisors(n)) ; end proc:
A190376 := proc(n) add(A067399(k), k=2^n..2^(n+1)-1) ; end proc: # R. J. Mathar, May 30 2011
CROSSREFS
Sequence in context: A320545 A232580 A133546 * A276785 A171844 A324971
KEYWORD
nonn,base,more
AUTHOR
N. J. A. Sloane, May 09 2011
STATUS
approved