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

Author

David Consiglio, Jr., May 29 2019

Keywords

• nonn
• base

Comments

All terms are zeroless (A052382).

Examples

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

Links

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

Crossrefs

Cf. A007602, A052382, A128212.

Programs

Magma

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

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 *)

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

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)