# A109941

Hans Havermann pxp at rogers.com
Fri Jul 22 03:42:02 CEST 2005

```%I A109941
%S A109941 45,2430,165150,12370500
%N A109941 Sum of all n-digit multiples of n.
%C A109941 a(n) ==0 (mod 45)
%e A109941 a(2) = 2430, a(2) = 10 +12+...+96+98 = 45*(10+98)/2.
%K A109941 base,more,nonn,new
%O A109941 1,1
%A A109941 Amarnath Murthy (amarnath_murthy(AT)yahoo.com), Jul 19 2005

In Mathematica:

Table[Sum[i, {i, n*Ceiling[(10^(n - 1))/n], 10^n - 1, n}], {n, 1, 30}]

{45, 2430, 165150, 12370500, 989955000, 82499850000, 7071428928571,
618749955000000, 55000000350000000, 4949999995500000000,
449999999955000000000, 41250000000150000000000,
3807692307689192307692307, 353571428571466428571428572,
32999999999999850000000000000, 3093749999999995500000000000000,
291176470588235280882352941176469,
27499999999999999950000000000000000,
2605263157894736841394736842105263156,
247499999999999999955000000000000000000,
23571428571428571428478571428571428571428,
2249999999999999999999500000000000000000000,
215217391304347826086958478260869565217391302,
20624999999999999999999850000000000000000000000,
1979999999999999999999995500000000000000000000000,
190384615384615384615384579615384615384615384615386,
18333333333333333333333333816666666666666666666666669,
1767857142857142857142857146642857142857142857142857144,
170689655172413793103448275872931034482758620689655172411,
16500000000000000000000000000150000000000000000000000000000}

Assuming I did this correctly, the mod-45 observation is not warranted.
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