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%I #16 Feb 18 2019 10:13:43
%S 1,4,12,31,75,175,393,864,1868,3978,8394
%N a(n) = sum (in ordinary arithmetic) of A067399(k), for k from 2^n to 2^(n+1)-1.
%C 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.
%H D. Applegate, M. LeBrun and N. J. A. Sloane, <a href="http://arxiv.org/abs/1107.1130">Dismal Arithmetic</a> [Note: we have now changed the name from "dismal arithmetic" to "lunar arithmetic" - the old name was too depressing]
%H <a href="/index/Di#dismal">Index entries for sequences related to dismal (or lunar) arithmetic</a>
%p read("transforms");
%p numbralADD := proc(a,b) option remember; ORnos(a,b) ; end proc:
%p 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:
%p 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:
%p 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:
%p A067399 := proc(n) nops(numbralDivisors(n)) ; end proc:
%p A190376 := proc(n) add(A067399(k),k=2^n..2^(n+1)-1) ; end proc: # _R. J. Mathar_, May 30 2011
%Y Cf. A067399, A188548.
%K nonn,base,more
%O 0,2
%A _N. J. A. Sloane_, May 09 2011
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