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A323731
a(n) is the number of numbers k whose n-th power has exactly k divisors.
5
1, 2, 2, 3, 4, 1, 2, 2, 2, 2, 5, 2, 4, 2, 1, 2, 5, 2, 2, 4, 2, 1, 2, 4, 2, 2, 2, 2, 5, 4, 2, 2, 2, 2, 2, 2, 2, 2, 2, 4, 3, 1, 5, 10, 3, 2, 5, 2, 2, 2, 1, 4, 2, 3, 1, 6, 2, 2, 2, 6, 4, 4, 3, 4, 2, 2, 5, 1, 2, 2, 5, 4, 5, 2, 3, 3, 1, 4, 2, 5, 2, 2, 2, 2, 2, 2, 1
OFFSET
0,2
COMMENTS
a(n) is the number of terms in row n of A323730.
Since 1^n = 1 has exactly 1 divisor for all n, a(n) >= 1.
A323732 lists the numbers j such that a(j) = 1 (i.e., such that A073049(j) = 0); for each such j, the only number k whose j-th power has exactly k divisors is 1.
A323733 lists the numbers j such that a(j) > 1 (i.e., such that A073049(j) > 0).
LINKS
EXAMPLE
a(0) = 1 because there is only one number k whose 0th power (k^0 = 1) has exactly k divisors (namely, k=1).
a(2) = 2 because there are two numbers k such that tau(k^2) = k: tau(1^2) = tau(1) = 1 and tau(3^2) = tau(9) = 3.
a(43) = 10 because there are 10 numbers k such that tau(k^43) = k: 1, 7569, 2197000, 4296680960, 11128700700, 16629093000, 223705109760, 19462344549120, 32521578186240, and 5580197619796800.
CROSSREFS
KEYWORD
nonn
AUTHOR
Jon E. Schoenfield, Jan 26 2019
STATUS
approved