A230103 Number of m such that m + (product of digits of m) equals n.

1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 2, 0, 2, 0, 2, 0, 2, 0, 2, 0, 2, 0, 1, 1, 1, 0, 2, 0, 1, 1, 1, 0, 1, 0, 1, 1, 0, 0, 2, 0, 1, 1, 1, 0, 1, 1, 1, 1, 0, 0, 3, 0, 0, 0, 1, 1, 1, 0, 1, 0, 2, 0, 2, 0, 0, 1, 1, 1, 1, 0, 2, 0, 0, 0, 2, 1, 0, 0, 1, 0, 3, 1, 0, 0, 0, 1, 2, 0, 1, 1, 1, 0, 1, 0, 1, 1, 0, 0, 2, 0, 2, 1, 3

Offset: 0

Author

N. J. A. Sloane, Oct 13 2013

Keywords

• nonn
• base

Comments

Number of times n appears in A230099.

Links

• Michel Marcus, Table of n, a(n) for n = 0..10000
• Index entries for Colombian or self numbers and related sequences

Crossrefs

Cf. A230099, A230104.

Programs

Maple

# Maple code for A230099, A230103, A230104, A230105
with(LinearAlgebra):
read transforms; # to get digprod
M:=1000;
lis1:=Array(0..M);
lis2:=Array(0..M);
ctmax:=4;
for i from 0 to ctmax do ct[i]:=Array(0..M); od:
for n from 0 to M do
m:=n+digprod(n);
lis1[n]:=m;
if (m <= M) then lis2[m]:=lis2[m]+1; fi;
od:
t1:=[seq(lis1[i],i=0..M)]; # A230099
t2:=[seq(lis2[i],i=0..M)]; # A230103
COMPl(t1); # A230104
for i from 1 to M do h:=lis2[i];
if h <= ctmax then ct[h]:=[op(ct[h]),i]; fi; od:
len:=nops(ct[0]); [seq(ct[0][i],i=1..len)]; # A230104 again
len:=nops(ct[1]); [seq(ct[1][i],i=1..len)]; # A230105

PARI

a(n) = if (n==0, return(1)); sum(k=1, n, k+vecprod(digits(k)) == n); \\ Michel Marcus, Sep 18 2020

Python

from math import prod
def b(n): return n + prod(map(int, str(n)))
def a(n): return sum(1 for m in range(n+1) if b(m) == n)
print([a(n) for n in range(103)]) # Michael S. Branicky, Jan 09 2023

Python

# faster version for initial segment of sequence
from math import prod
from collections import Counter
def b(n): return n + prod(map(int, str(n)))
def aupto(n):
    c = Counter(b(m) for m in range(n+1))
    return [c[k] for k in range(n+1)]
print(aupto(102)) # Michael S. Branicky, Jan 09 2023