A190376 a(n) = sum (in ordinary arithmetic) of A067399(k), for k from 2^n to 2^(n+1)-1.

1, 4, 12, 31, 75, 175, 393, 864, 1868, 3978, 8394

Offset: 0

Author

N. J. A. Sloane, May 09 2011

Keywords

• nonn
• base
• more

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]
• Index entries for sequences related to dismal (or lunar) arithmetic

Crossrefs

Cf. A067399, A188548.

Programs

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