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A364813
Generalized positive integers (see formula section).
1
1, 2, 3, 16, 5, 36, 7, 256, 81, 100, 11, 3456, 13, 196, 225, 32768, 17, 17496, 19, 16000, 441, 484, 23, 1327104, 625, 676, 6561, 43904, 29, 810000, 31, 2097152, 1089, 1156, 1225, 362797056, 37, 1444, 1521, 10240000, 41, 3111696, 43, 170368, 273375, 2116, 47, 8153726976, 2401, 625000
OFFSET
1,2
LINKS
Jeffrey C. Lagarias and Wijit Yangjit, The factorial function and generalizations, extended, arXiv:2310.12949 [math.NT], 2023. See Section 7.2 pp. 20-21 and Table 1 p. 29.
FORMULA
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).
PROG
(PARI) f(n, b) = sum(i=1, logint(n, b), n\b^i);
d(n, b) = f(n, b)-f(n-1, b);
a(n) = prod(b=2, n, b^d(n, b));
CROSSREFS
Cf. A363838 (also uses gamma).
Sequence in context: A326578 A103390 A167761 * A176029 A218323 A369893
KEYWORD
nonn
AUTHOR
Michel Marcus, Oct 21 2023
STATUS
approved