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

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);

Crossrefs

Cf. A275170.

Sequence in context: A230450 A247989 A126078 * A028299 A205628 A203934

Adjacent sequences: A275168 A275169 A275170 * A275172 A275173 A275174

Keyword

nonn,base,more

Author

Paolo P. Lava, Jul 19 2016

Extensions

a(18)-a(26) from Giovanni Resta, Jul 21 2016

Status

approved