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A038701 Prime powers q for which f(g(m(q))) = m(q), where f = A051703, g = A008475 and m = A003418. 0
2, 3, 4, 5, 7, 8, 9, 11, 13, 16, 17, 19, 23, 25, 29, 31, 32, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 103, 107, 109, 113 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,1
COMMENTS
These functions are defined for all natural numbers > 1 by: g(x) = Sum (p_j^k_j) where x = Product (p_j^k_j) is prime factorization of x (A008475); f(n) = max{x:g(x)=n} (A051703); m(n) = lcm(1,2,3,...,n) (A003418).
There are no more prime powers in the list <= 199. Conjecture: The sequence is finite, i.e., f(g(m(q))) > m(q) for sufficiently great prime powers q.
No other terms below 409. - Max Alekseyev, Sep 05 2023
LINKS
EXAMPLE
27 is not in the list because m(27) = 2^4*3^3*5^2*7*11*13*17*19*23, g(m(27))=158, f(158) = 3*5*7*11*13*17*19*23*29*31 > m(27).
CROSSREFS
Sequence in context: A164336 A348263 A115919 * A127072 A341089 A056781
KEYWORD
nonn,more
AUTHOR
Vladeta Jovovic, May 01 2000
EXTENSIONS
Offset changed to 1 by Jinyuan Wang, Mar 16 2020
STATUS
approved

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Last modified March 18 22:56 EDT 2024. Contains 370952 sequences. (Running on oeis4.)