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A249346 The exponent of the highest power of 6 dividing the product of the elements on the n-th row of Pascal's triangle.

%I A249346 #26 Feb 07 2025 15:14:42
%S A249346 0,0,0,0,1,0,4,0,0,10,10,4,13,8,3,0,6,0,28,20,12,24,15,6,20,10,0,16,
%T A249346 47,22,26,0,30,48,33,18,73,56,39,40,42,24,47,28,9,54,57,16,62,40,18,
%U A249346 46,23,0,82,32,84,94,87,44,92,52,36,0,102,72,107,76,45,82,50,18,128,94,60,100,65,30,72,36,0
%N A249346 The exponent of the highest power of 6 dividing the product of the elements on the n-th row of Pascal's triangle.
%C A249346 Sounds good with MIDI player set to FX-7.
%H A249346 Antti Karttunen, <a href="/A249346/b249346.txt">Table of n, a(n) for n = 0..7775</a>
%F A249346 a(n) = min(A187059(n), A249343(n)).
%F A249346 a(n) = A122841(A001142(n)).
%F A249346 Other identities:
%F A249346 a(n) = 0 when A249151(n) < 3.
%t A249346 IntegerExponent[#,6]&/@Times@@@Table[Binomial[n,k],{n,0,80},{k,0,n}] (* _Harvey P. Dale_, Nov 21 2023 *)
%o A249346 (PARI)
%o A249346 A249346(n) = { my(b, s2, s3); s2 = 0; s3 = 0; for(k=0, n, b = binomial(n, k); s2 += valuation(b, 2); s3 += valuation(b, 3)); min(s2,s3); };
%o A249346 for(n=0, 7775, write("b249346.txt", n, " ", A249346(n)));
%o A249346 (Scheme)
%o A249346 (define (A249346 n) (min (A187059 n) (A249343 n)))
%o A249346 (Scheme)
%o A249346 (define (A249346 n) (A122841 (A001142 n)))
%o A249346 (Haskell)
%o A249346 a249346 = a122841 . a001142  -- _Reinhard Zumkeller_, Mar 16 2015
%Y A249346 Minimum of terms A187059(n) and A249343(n).
%Y A249346 Cf. A001142, A122841, A249151.
%K A249346 nonn,hear,look
%O A249346 0,7
%A A249346 _Antti Karttunen_, Oct 31 2014