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%I #14 Oct 22 2023 01:25:36
%S 1,2,3,16,5,36,7,256,81,100,11,3456,13,196,225,32768,17,17496,19,
%T 16000,441,484,23,1327104,625,676,6561,43904,29,810000,31,2097152,
%U 1089,1156,1225,362797056,37,1444,1521,10240000,41,3111696,43,170368,273375,2116,47,8153726976,2401,625000
%N Generalized positive integers (see formula section).
%H Michel Marcus, <a href="/A364813/b364813.txt">Table of n, a(n) for n = 1..10000</a>
%H Jeffrey C. Lagarias and Wijit Yangjit, <a href="https://arxiv.org/abs/2310.12949">The factorial function and generalizations, extended</a>, arXiv:2310.12949 [math.NT], 2023. See Section 7.2 pp. 20-21 and Table 1 p. 29.
%F a(n) = Product_{b=2..n} b^d(n,b) where d(n,b)=gamma(n,b)-gamma(n-1,b) and gamma(n,b) = Sum_{i>=1} floor(n/b^i).
%o (PARI) f(n, b) = sum(i=1, logint(n, b), n\b^i);
%o d(n,b) = f(n,b)-f(n-1,b);
%o a(n) = prod(b=2, n, b^d(n,b));
%Y Cf. A363838 (also uses gamma).
%K nonn
%O 1,2
%A _Michel Marcus_, Oct 21 2023