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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 (list; graph; refs; listen; history; text; internal format)



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.


Table of n, a(n) for n=0..10.

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



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


Cf. A067399, A188548.

Sequence in context: A320545 A232580 A133546 * A276785 A171844 A324971

Adjacent sequences:  A190373 A190374 A190375 * A190377 A190378 A190379




N. J. A. Sloane, May 09 2011



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Last modified January 25 05:31 EST 2021. Contains 340416 sequences. (Running on oeis4.)