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A339514
Number of subsets of {1..n} whose elements have the same number of divisors.
3
1, 2, 3, 5, 6, 10, 11, 19, 21, 23, 27, 43, 44, 76, 84, 100, 101, 165, 167, 295, 299, 331, 395, 651, 652, 656, 784, 1040, 1048, 1560, 1562, 2586, 2602, 3114, 4138, 6186, 6187, 8235, 12331, 20523, 20527, 24623, 24631, 32823, 32855, 32919, 49303, 65687, 65688
OFFSET
0,2
LINKS
Eric Weisstein's World of Mathematics, Divisor
FORMULA
a(0) = 1, a(n) = a(n-1) + 2^A047983(n). - Sebastian Karlsson, Dec 26 2020
EXAMPLE
a(8) = 21 subsets: {}, {1}, {2}, {3}, {4}, {5}, {6}, {7}, {8}, {2, 3}, {2, 5}, {2, 7}, {3, 5}, {3, 7}, {5, 7}, {6, 8}, {2, 3, 5}, {2, 3, 7}, {2, 5, 7}, {3, 5, 7} and {2, 3, 5, 7}.
PROG
(Python)
from sympy import divisors
def test(n):
if n<2: return n-1
return len(divisors(n))
def a(n):
tests = [test(i) for i in range(n+1)]
return sum(2**tests.count(v)-1 for v in set(tests))
print([a(n) for n in range(49)]) # Michael S. Branicky, Dec 07 2020
CROSSREFS
KEYWORD
nonn
AUTHOR
Ilya Gutkovskiy, Dec 07 2020
EXTENSIONS
a(25)-a(48) from Michael S. Branicky, Dec 07 2020
STATUS
approved