A268444 a(n) = Product_{i=0..k}(n_i+1) where n = Sum_{i=0..k}n_i*4^i is the base-4 representation of n.
1, 2, 3, 4, 2, 4, 6, 8, 3, 6, 9, 12, 4, 8, 12, 16, 2, 4, 6, 8, 4, 8, 12, 16, 6, 12, 18, 24, 8, 16, 24, 32, 3, 6, 9, 12, 6, 12, 18, 24, 9, 18, 27, 36, 12, 24, 36, 48, 4, 8, 12, 16, 8, 16, 24, 32, 12, 24, 36, 48, 16, 32, 48, 64, 2, 4, 6, 8, 4, 8, 12, 16, 6, 12, 18, 24
Offset: 0
Examples
The base-4 representation of 10 is (2,2) so a(10) = (2+1)*(2+1) = 9.
Links
- Antti Karttunen, Table of n, a(n) for n = 0..16384
- Tyler Ball, Tom Edgar, and Daniel Juda, Dominance Orders, Generalized Binomial Coefficients, and Kummer's Theorem, Mathematics Magazine, Vol. 87, No. 2, April 2014, pp. 135-143.
Programs
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PARI
a(n) = my(d=digits(n,4)); prod(k=1, #d, d[k]+1); \\ Michel Marcus, Feb 05 2016
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Python
from math import prod from gmpy2 import digits def A268444(n): s = digits(n,4) return prod((int(d)+1)**s.count(d) for d in '123') # Chai Wah Wu, Apr 24 2025
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Sage
[prod(x+1 for x in n.digits(4)) for n in [0..75]]
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Scheme
(define (A268444 n) (if (zero? n) 1 (let ((d (mod n 4))) (* (+ 1 d) (A268444 (/ (- n d) 4)))))) ;; For R6RS standard. Use modulo instead of mod in older Schemes like MIT/GNU Scheme. - Antti Karttunen, May 28 2017
Formula
a(n) = Product_{i=0..k}(n_i+1) where n = Sum_{i=0..k}n_i*4^i.
Comments