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A249153 Exponent of 2 in the hyperfactorial of 2n: a(n) = A007814(A002109(2n)).

%I A249153 #20 Sep 10 2024 08:44:18
%S A249153 0,2,10,16,40,50,74,88,152,170,210,232,304,330,386,416,576,610,682,
%T A249153 720,840,882,970,1016,1208,1258,1362,1416,1584,1642,1762,1824,2208,
%U A249153 2274,2410,2480,2696,2770,2922,3000,3320,3402,3570,3656,3920,4010,4194,4288,4768,4866,5066,5168,5480,5586,5802,5912
%N A249153 Exponent of 2 in the hyperfactorial of 2n: a(n) = A007814(A002109(2n)).
%H A249153 Chai Wah Wu, <a href="/A249153/b249153.txt">Table of n, a(n) for n = 0..10000</a>
%F A249153 a(n) = A249152(2*n) = A007814(A002109(2*n)).
%F A249153 a(n) = 2*A143157(n).
%F A249153 a(n) ~ 2*n^2. - _Amiram Eldar_, Sep 10 2024
%t A249153 Table[IntegerExponent[Hyperfactorial[2*n], 2], {n, 0, 55}] (* _Amiram Eldar_, Sep 10 2024 *)
%o A249153 (Scheme, two alternative versions)
%o A249153 (define (A249153 n) (* 2 (A143157 n)))
%o A249153 (define (A249153 n) (A249152 (+ n n)))
%o A249153 (Python)
%o A249153 from sympy import multiplicity
%o A249153 A249153_list, n = [0], 0
%o A249153 for i in range(2,20002,2):
%o A249153     n += multiplicity(2,i)*i
%o A249153     A249153_list.append(n) # _Chai Wah Wu_, Aug 21 2015
%Y A249153 Bisection of A249152.
%Y A249153 Cf. A002109, A007814, A143157, A069895 (first differences).
%K A249153 nonn
%O A249153 0,2
%A A249153 _Antti Karttunen_, Oct 25 2014