A275171 - OEIS

A275171

Partition the j digits of n into blocks of k, with 1 <= k <= j-1, starting at left and multiply. Sum of these numbers equals n.

396, 1064, 1518, 1545, 4318, 4345, 4563, 12154, 21154, 145250, 517150, 532315, 43321250, 66710504, 175401008, 407902400, 492701500, 1148032202, 10144502500, 35308402400, 44916701500, 90751434020, 101445025000, 353084024000, 449167015000, 907514340200

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OFFSET

1,1

COMMENTS

The number of partitions of k digits are [j-(j mod k)]/k. If j is not a multiple of k the last partition has j mod k digits. E.g.: the partitions of 3 digits of 5573670 are 557 and 367 plus a partition of one digit, 0 (here j=7 and k=3). - Paolo P. Lava, Aug 04 2016

LINKS

Table of n, a(n) for n=1..26.

EXAMPLE

3*9*6 + 39*6 = 396;

1*0*6*4 + 10*64 + 106*4 = 1064;

1*2*1*5*4 + 12*15*4 + 121*54 + 1215*4 = 12154.

MAPLE

P:=proc(q) local a, b, c, d, j, k, n;

for n from 1 to q do c:=0; for k from 1 to ilog10(n) do a:=1; b:=n; d:=ilog10(n)+1;

for j from 1 to trunc(d/k) do a:=a*(trunc(n/10^(d-j*k)) mod 10^k); od;

if d-trunc(d/k)*k>0 then a:=a*(n mod 10^(d-trunc(d/k)*k)); fi;

c:=c+a; od; if n=c then print(n); fi; od; end: P(10^6);