

A038701


Prime powers q for which f(l(m(q)))=m(q).


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
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OFFSET

0,1


COMMENTS

These functions are defined for all natural numbers >1 by: l(x)=Sum (p_j^k_j) where x=Product (p_j^k_j) is prime factorization of x (A008475); f(n)=max{x:l(x)=n} (A051703); m(n)=lcm{1,2,3,...,n} (A003418).


LINKS

Table of n, a(n) for n=0..31.
D. W. Wilson, Answers to sci.math questions


EXAMPLE

27 is not in the list because m(27)=2^4*3^3*5^2*7*11*13*17*19*23, l(m(27))=158, f(158)=3*5*7*11*13*17*19*23*29*31>m(27);


CROSSREFS

Cf. A000961.
Sequence in context: A096165 A164336 A115919 * A127072 A056781 A079446
Adjacent sequences: A038698 A038699 A038700 * A038702 A038703 A038704


KEYWORD

more,nonn


AUTHOR

Vladeta Jovovic, May 01 2000


EXTENSIONS

There are no more prime powers in the list <=199. Conjecture: The sequence is finite, i.e. f(l(m(q)))>m(q) for sufficiently great prime powers q.


STATUS

approved



