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

0,11

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

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

Prog

(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

Crossrefs

Cf. A230099, A230104.

Sequence in context: A096972 A101227 A277162 * A267602 A021499 A176742

Adjacent sequences: A230100 A230101 A230102 * A230104 A230105 A230106

Keyword

nonn,base

Author

N. J. A. Sloane, Oct 13 2013

Status

approved