A038701 Prime powers q for which f(g(m(q))) = m(q), where f = A051703, g = A008475 and m = A003418.

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

Offset: 1

Author

Vladeta Jovovic, May 01 2000

Keywords

• nonn
• more

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

Examples

			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).
		

Links

• D. W. Wilson, Answers to sci.math questions

Crossrefs

Cf. A000961, A003418, A008475, A051703.

Extensions

Offset changed to 1 by Jinyuan Wang, Mar 16 2020