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 A232541 Multiplicative Smith numbers: Composite numbers n such that the product of nonzero digits of n = product of nonzero digits of prime factors of n. 1
 4, 6, 8, 9, 95, 159, 195, 249, 326, 762, 973, 995, 998, 1057, 1086, 1111, 1189, 1236, 1255, 1337, 1338, 1383, 1389, 1395, 1419, 1509, 2139, 2248, 2623, 2679, 2737, 2928, 2949, 3029, 3065, 3202, 3344, 3345, 3419, 3432, 3437, 3464, 3706, 3945, 4344, 4502 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS They follow the same formula for Smith numbers, however, instead of addition, we have multiplication (only nonzero digits are included). Trivially, prime numbers satisfy this property but are not included in the sequence. LINKS T. D. Noe, Table of n, a(n) for n = 1..1000 EXAMPLE 1236 is a member of this sequence because 1236 = 2*2*3*103 and 1*2*3*6 = 2*2*3*1*3 (zeros are not included). 998 is a member of this sequence because 998 = 2*499 and 9*9*8 = 2*4*9*9. MATHEMATICA f[n_] := Times @@ DeleteCases[IntegerDigits[n], 0]; pFactors[n_] := Module[{f = FactorInteger[n]}, Flatten[ConstantArray @@@ f]]; Select[Range[2, 10000], ! PrimeQ[#] && f[#] == Times @@ f /@ pFactors[#] &] (* T. D. Noe, Nov 28 2013 *) PROG (Python) import sympy from sympy import isprime from sympy import factorint def DigitProd(x):     prod = 1     for i in str(x):         if i != '0':             prod *= int(i)     return prod def f(x):     lst = []     for n in range(len(list(factorint(x)))):         lst.append(str(list(factorint(x))[n])*list(factorint(x).values())[n])     string = ''     for i in lst:         string += i     prod = 1     for a in string:         if a != '0':             prod *= int(a)     if prod == DigitProd(x):         return True x = 4 while x < 10**3:     if not isprime(x):         if f(x):             print(x)     x += 1 (Sage) def prodPrimeDig(x):     F=factor(x)     T=[item for sublist in [[y[0]]*y[1] for y in F] for item in sublist]     return prod([prod(filter(lambda a: a!=0, h.digits(base=10))) for h in T]) n=3345 #Change n for more digits [k for k in [1..n] if prod(filter(lambda a: a!=0, k.digits(base=10)))==prodPrimeDig(k) and not(is_prime(k))] # Tom Edgar, Nov 26 2013 CROSSREFS Cf. A006753, A051801. Sequence in context: A029581 A202262 A202266 * A076612 A182775 A046354 Adjacent sequences:  A232538 A232539 A232540 * A232542 A232543 A232544 KEYWORD nonn,base,easy,changed AUTHOR Derek Orr, Nov 25 2013 EXTENSIONS Extended by T. D. Noe, Nov 28 2013 STATUS approved

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Last modified March 31 16:23 EDT 2020. Contains 333151 sequences. (Running on oeis4.)