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A209237
Number of practical numbers not exceeding 2^n.
3
1, 2, 3, 5, 7, 13, 21, 36, 61, 113, 202, 368, 667, 1218, 2268, 4222, 7959, 15057, 28480, 53742, 101770, 193406, 368610, 703596, 1347122, 2587174, 4981200, 9602184, 18548787, 35847883, 69321177, 134195809, 260023008, 504022592, 977757822, 1897859108, 3687288292, 7169361994
OFFSET
0,2
COMMENTS
Motivated by Sun's conjecture concerning the asymptotics of A005153.
Up to 10^6, there are 97385 (9.7%), up to 10^7 there are 829157 (8.3%) practical numbers.
FORMULA
a(n) = 1 + Sum_{k=0..n-1} A214932(k). - Amiram Eldar, May 05 2024
a(n) = A225559(2^n). - David A. Corneth, May 05 2024
PROG
(PARI) a(n)=sum(k=1, 2^(n-1), is_A005153(2*k), 1)
CROSSREFS
KEYWORD
nonn
AUTHOR
M. F. Hasler, Jan 13 2013
EXTENSIONS
a(26)-a(30) from Jinyuan Wang, Mar 02 2020
a(31)-a(37) from Amiram Eldar, May 05 2024
STATUS
approved