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

%I A308472 #26 May 22 2025 10:21:48
%S A308472 1,2,3,4,5,6,7,8,9,11,12,15,24,25,28,36,52,54,63,99,111,112,115,125,
%T A308472 126,132,138,152,154,156,162,165,168,182,187,189,198,212,215,216,224,
%U A308472 234,251,252,255,261,264,276,279,297,312,318,324,333,342,354,369,372,396,432,441
%N A308472 Numbers that are divisible by the sum of the digits of the product of their digits.
%C A308472 All terms are zeroless (A052382).
%H A308472 David Consiglio, Jr., <a href="/A308472/b308472.txt">Table of n, a(n) for n = 1..6253</a>
%e A308472 2771 is a term of this sequence because 2*7*7*1 = 98 --> 9 + 8 = 17 --> 2771 / 17 = 163.
%p A308472 d:= n-> convert(n, base, 10):
%p A308472 q:= n-> (m-> m>0 and irem(n, add(j, j=d(m)))=0)(mul(i, i=d(n))):
%p A308472 select(q, [$1..500])[];  # _Alois P. Heinz_, May 29 2019
%t A308472 Select[Range[500],DigitCount[#,10,0]==0&&Divisible[#,Total[ IntegerDigits[ Times@@IntegerDigits[#]]]]&] (* _Harvey P. Dale_, Jan 24 2021 *)
%o A308472 (Python)
%o A308472 def dprod(n):
%o A308472     x = str(n)
%o A308472     start = 1
%o A308472     for q in x:
%o A308472         start *= int(q)
%o A308472     return start
%o A308472 def dsum(n):
%o A308472     x = str(n)
%o A308472     start = 0
%o A308472     for q in x:
%o A308472         start += int(q)
%o A308472     return start
%o A308472 seq_1 = [n for n in range(1,10000) if dprod(n) != 0 and n % (dsum(dprod(n))) == 0]
%o A308472 print(seq_1)
%o A308472 (PARI) spd(n) = my(d=digits(n)); sumdigits(vecprod(d)); \\ A128212
%o A308472 isok(n) = my(p=spd(n)); p && (n % p == 0); \\ _Michel Marcus_, May 29 2019
%o A308472 (Magma) [n:n in [1..450]| not 0 in Intseq(n) and IsIntegral(n/(&+Intseq((&*(Intseq(n))))))]; // _Marius A. Burtea_, May 31 2019
%Y A308472 Cf. A007602, A052382, A128212.
%K A308472 nonn,base
%O A308472 1,2
%A A308472 _David Consiglio, Jr._, May 29 2019