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 A007954 Product of decimal digits of n. 236
 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 0, 2, 4, 6, 8, 10, 12, 14, 16, 18, 0, 3, 6, 9, 12, 15, 18, 21, 24, 27, 0, 4, 8, 12, 16, 20, 24, 28, 32, 36, 0, 5, 10, 15, 20, 25, 30, 35, 40, 45, 0, 6, 12, 18, 24, 30, 36, 42, 48, 54, 0, 7, 14, 21, 28, 35, 42, 49, 56, 63, 0, 8, 16, 24, 32, 40, 48, 56, 64, 72, 0, 9, 18, 27, 36, 45, 54, 63, 72, 81, 0, 0, 0, 0, 0, 0, 0, 0 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,3 COMMENTS Moebius transform of A093811(n). a(n) = A093811(n) * A008683(n), where operation * denotes Dirichlet convolution, namely b(n) * c(n) = Sum_{d|n} b(d) * c(n/d). Simultaneously holds Dirichlet multiplication: a(n) * A000012(n) = A093811(n). - Jaroslav Krizek, Mar 22 2009 Apart from the 0's, all terms are in A002473. Further, for all m in A002473 there is some n such that a(n) = m, see A096867. - Charles R Greathouse IV, Sep 29 2013 a(n) = 0 asymptotically almost surely, namely for all n except for the set of numbers without digit '0'; this set is of density zero, since it is less and less probable to have no '0' as the number of digits of n grows. (See also A054054.) - M. F. Hasler, Oct 11 2015 LINKS N. J. A. Sloane, Table of n, a(n) for n = 0..10000 Rigoberto Flórez, Robinson A. Higuita, Antara Mukherjee, Alternating Sums in the Hosoya Polynomial Triangle, Article 14.9.5 Journal of Integer Sequences, Vol. 17 (2014). Florentin Smarandache, Only Problems, Not Solutions!. FORMULA A000035(a(A014261(n))) = 1. - Reinhard Zumkeller, Nov 30 2007 a(n) = abs(A187844(n)). - Reinhard Zumkeller, Mar 14 2011 a(n) > 0 if and only if A054054(n) > 0. a(n) = d in {1, ..., 9} if n = (10^k - 1)/9 + (d - 1)*10^m = A002275(k) + (d - 1)*A011557(m) for some k > m >= 0. The statement holds with "if and only if" for d in {1, 2, 3, 5, 7}. For d = 4, 6, 8 or 9, one has a(n) = d if n = (10^k - 1)/9 + (a - 1)*10^m + (b - 1)*10^p with integers k > m > p >= 0 and a, b > 0 such that d = a*b. - M. F. Hasler, Oct 11 2015 From Robert Israel, May 17 2016: (Start) G.f.: Sum_{n >= 0} Product_{j = 0..n} Sum_{k = 1..9} k*x^(k*10^j). G.f. satisfies A(x) = (x + 2*x^2 + ... + 9*x^9)*(1 + A(x^10)). (End) MAPLE A007954 := proc(n::integer)     if n = 0 then         0;     else         mul( d, d=convert(n, base, 10)) ;     end if; end proc: # R. J. Mathar, Oct 02 2019 MATHEMATICA Array[Times @@ IntegerDigits@ # &, 108, 0] (* Robert G. Wilson v, Mar 15 2011 *) PROG (PARI) A007954(n)= { local(resul = n % 10); n \= 10; while( n > 0, resul *= n %10; n \= 10; ); return(resul); } \\ R. J. Mathar, May 23 2006, edited by M. F. Hasler, Apr 23 2015 (PARI) A007954(n)=prod(i=1, #n=Vecsmall(Str(n)), n[i]-48) \\ (...eval(Vec(...)), n[i]) is about 50% slower; (...digits(n)...) about 6% slower. \\ M. F. Hasler, Dec 06 2009 (PARI) a(n)=if(n, factorback(digits(n)), 0) \\ Charles R Greathouse IV, Apr 14 2020 (Haskell) a007954 n | n < 10 = n           | otherwise = m * a007954 n' where (n', m) = divMod n 10 -- Reinhard Zumkeller, Oct 26 2012, Mar 14 2011 (MAGMA)  cat [&*Intseq(n): n in [1..110]]; // Vincenzo Librandi, Jan 03 2020 (Scala) (0 to 99).map(_.toString.toCharArray.map(_ - 48).scanRight(1)(_ * _).head) // Alonso del Arte, Apr 14 2020 CROSSREFS Cf. A031347 (different from A035930), A007953, A007602, A010888, A093811, A008683, A000012, A061076 (partial sums), A230099. Cf. A051802 (ignoring zeroes). Sequence in context: A087471 A128212 A187844 * A079475 A081286 A080867 Adjacent sequences:  A007951 A007952 A007953 * A007955 A007956 A007957 KEYWORD nonn,base,easy,nice,hear AUTHOR R. Muller EXTENSIONS Error in term 25 corrected, Nov 15 1995 STATUS approved

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Last modified September 18 07:26 EDT 2020. Contains 337166 sequences. (Running on oeis4.)