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

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

1,2

Comments

All terms are zeroless (A052382).

Links

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

Example

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

Maple

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

Mathematica

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

Prog

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

Crossrefs

Cf. A007602, A052382, A128212.

Sequence in context: A063527 A209933 A182183 * A064700 A180484 A007602

Adjacent sequences: A308469 A308470 A308471 * A308473 A308474 A308475

Keyword

nonn,base

Author

David Consiglio, Jr., May 29 2019

Status

approved