A128212 -id:A128212 - cp's OEIS frontend

A128290 If p(x) is the product of the digits of the number x and s(x) the sum of the digits then the sequence lists all the numbers k for which p(s(k)) = s(p(k)), with k >= 1.

1, 2, 3, 4, 5, 6, 7, 8, 9, 22, 36, 63, 109, 123, 132, 158, 185, 190, 199, 208, 213, 231, 280, 289, 298, 307, 312, 321, 333, 370, 406, 458, 460, 469, 485, 496, 505, 518, 548, 550, 556, 559, 565, 581, 584, 595, 604, 640, 649, 655, 667, 676, 694, 703, 730, 766, 802

Offset: 1

Paolo P. Lava and Giorgio Balzarotti, May 04 2007

			496 is a term: s(496) = 4+9+6 = 19, p(s(496)) = 1*9 = 9, p(496) = 4*9*6 = 216, s(p(496)) = 2+1+6 = 9.
845 is a term: s(845) = 8+4+5 = 17, p(s(845)) = 1*7 = 7, p(845) = 8*4*5 = 160, s(p(845)) = 1+6+0 = 7.
From _Jon E. Schoenfield_, Jun 15 2024: (Start)
Expressed more visually:
.
          Sum                         Sum
   496 --------> 19            845 --------> 17
    |    4+9+6    |             |    8+4+5    |
  P | 4         P |           P | 8         P |
  r | *         r | 1         r | *         r | 1
  o | 9         o | *         o | 4         o | *
  d | *         d | 9         d | *         d | 7
    | 6           |             | 5           |
    v     Sum     v             v     Sum     v
   216 -------->  9            160 -------->  7
         2+1+6                       1+6+0
(End)

Michael S. Branicky, Table of n, a(n) for n = 1..10000

Cf. A007953, A007954, A128212, A128244.

P:=proc(q) local a,b,c; a:=convert(q,base,10): b:=convert(a,`+`): c:=convert(a,`*`):
if convert(convert(b,base,10),`*`)=convert(convert(c,base,10),`+`) then q; fi; end: seq(P(i),i=1..10^3); # Paolo P. Lava, Jun 15 2024

p[n_] := Times @@ IntegerDigits[n]; Select[Range[1000], p[DigitSum[#]] == DigitSum[p[#]] &] (* Paolo Xausa, Jun 17 2024 *)

from math import prod
def ok(n):
    d = list(map(int, str(n)))
    p, s = prod(d), sum(d)
    return sum(map(int, str(p))) == prod(map(int, str(s)))
print([k for k in range(1, 803) if ok(k)]) # Michael S. Branicky, Jun 15 2024

A308472 Numbers that are divisible by the sum of the digits of the product of their digits.

Original entry on oeis.org

1, 2, 3, 4, 5, 6, 7, 8, 9, 11, 12, 15, 24, 25, 28, 36, 52, 54, 63, 99, 111, 112, 115, 125, 126, 132, 138, 152, 154, 156, 162, 165, 168, 182, 187, 189, 198, 212, 215, 216, 224, 234, 251, 252, 255, 261, 264, 276, 279, 297, 312, 318, 324, 333, 342, 354, 369, 372, 396, 432, 441

Offset: 1

David Consiglio, Jr., May 29 2019

All terms are zeroless (A052382).

			2771 is a term of this sequence because 2*7*7*1 = 98 --> 9 + 8 = 17 --> 2771 / 17 = 163.

David Consiglio, Jr., Table of n, a(n) for n = 1..6253

Cf. A007602, A052382, A128212.

[n:n in [1..450]| not 0 in Intseq(n) and IsIntegral(n/(&+Intseq((&*(Intseq(n))))))]; // Marius A. Burtea, May 31 2019

d:= n-> convert(n, base, 10):
q:= n-> (m-> m>0 and irem(n, add(j, j=d(m)))=0)(mul(i, i=d(n))):
select(q, [$1..500])[];  # Alois P. Heinz, May 29 2019

Select[Range[500],DigitCount[#,10,0]==0&&Divisible[#,Total[ IntegerDigits[ Times@@IntegerDigits[#]]]]&] (* Harvey P. Dale, Jan 24 2021 *)

spd(n) = my(d=digits(n)); sumdigits(vecprod(d)); \\ A128212
isok(n) = my(p=spd(n)); p && (n % p == 0); \\ Michel Marcus, May 29 2019

def dprod(n):
    x = str(n)
    start = 1
    for q in x:
        start *= int(q)
    return start
def dsum(n):
    x = str(n)
    start = 0
    for q in x:
        start += int(q)
    return start
seq_1 = [n for n in range(1,10000) if dprod(n) != 0 and n % (dsum(dprod(n))) == 0]
print(seq_1)

cp's OEIS Frontend

A128290 If p(x) is the product of the digits of the number x and s(x) the sum of the digits then the sequence lists all the numbers k for which p(s(k)) = s(p(k)), with k >= 1.

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