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

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, 47, 22, 26, 0, 30, 48, 33, 18, 73, 56, 39, 40, 42, 24, 47, 28, 9, 54, 57, 16, 62, 40, 18, 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

Offset

0,7

Comments

Sounds good with MIDI player set to FX-7.

Links

Antti Karttunen, Table of n, a(n) for n = 0..7775

Formula

a(n) = min(A187059(n), A249343(n)).

a(n) = A122841(A001142(n)).

Other identities:

a(n) = 0 when A249151(n) < 3.

Mathematica

IntegerExponent[#, 6]&/@Times@@@Table[Binomial[n, k], {n, 0, 80}, {k, 0, n}] (* Harvey P. Dale, Nov 21 2023 *)

Prog

(PARI)
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); };
for(n=0, 7775, write("b249346.txt", n, " ", A249346(n)));
(Scheme, two alternative implementations)
(define (A249346 n) (min (A187059 n) (A249343 n)))
(define (A249346 n) (A122841 (A001142 n)))
(Haskell)
a249346 = a122841 . a001142  -- Reinhard Zumkeller, Mar 16 2015

Crossrefs

Minimum of terms A187059(n) and A249343(n).

Cf. A001142, A122841, A249151.

Sequence in context: A127319 A272626 A271910 * A035539 A178517 A049207

Adjacent sequences: A249343 A249344 A249345 * A249347 A249348 A249349

Keyword

nonn,hear,look

Author

Antti Karttunen, Oct 31 2014

Status

approved