A249347 The exponent of the highest power of 7 dividing the product of the elements on the n-th row of Pascal's triangle.

0, 0, 0, 0, 0, 0, 0, 6, 5, 4, 3, 2, 1, 0, 12, 10, 8, 6, 4, 2, 0, 18, 15, 12, 9, 6, 3, 0, 24, 20, 16, 12, 8, 4, 0, 30, 25, 20, 15, 10, 5, 0, 36, 30, 24, 18, 12, 6, 0, 90, 82, 74, 66, 58, 50, 42, 89, 80, 71, 62, 53, 44, 35, 88, 78, 68, 58, 48, 38, 28, 87, 76, 65, 54, 43, 32, 21, 86, 74, 62, 50, 38, 26, 14, 85, 72, 59, 46, 33, 20, 7, 84, 70, 56, 42, 28, 14, 0

Offset

0,8

Links

Antti Karttunen, Table of n, a(n) for n = 0..2400

Jeffrey C. Lagarias and Harsh Mehta, Products of binomial coefficients and unreduced Farey fractions, arXiv:1409.4145 [math.NT], 2014.

Formula

a(n) = A214411(A001142(n)).

a(n) = Sum_{k=0..n} A214411(binomial(n,k)).

a(n) = Sum_{i=1..n} (2*i-n-1)*v_7(i), where v_7(i) = A214411(i) is the exponent of the highest power of 7 dividing i. - Ridouane Oudra, Jun 03 2022

Prog

(PARI)
allocatemem(234567890);
A249347(n) = sum(k=0, n, valuation(binomial(n, k), 7));
for(n=0, 2400, write("b249347.txt", n, " ", A249347(n)));
(Scheme, two alternative implementations)
(define (A249347 n) (A214411 (A001142 n)))
(define (A249347 n) (add (lambda (n) (A214411 (A007318 n))) (A000217 n) (A000096 n)))
(define (add intfun lowlim uplim) (let sumloop ((i lowlim) (res 0)) (cond ((> i uplim) res) (else (sumloop (+ 1 i) (+ res (intfun i)))))))

Crossrefs

Row 4 of array A249421.

Cf. A001142, A007318, A214411, A187059, A249343, A249345.

Sequence in context: A023448 A307337 A031055 * A284805 A225660 A031056

Adjacent sequences: A249344 A249345 A249346 * A249348 A249349 A249350

Keyword

nonn

Author

Antti Karttunen, Oct 28 2014

Status

approved