OFFSET
1,3
COMMENTS
In the definition, replace "e_i*n^(i-1)" with "e_i*x^(i-1)" for all i to define a function P:N+ -> N[x]. If we extend this definition to positive rationals by allowing negative e_i, P(.) becomes an isomorphism between positive rationals under multiplication and polynomials over Z under addition. We can use P to generalize A001222, A048675 and A054841: evaluate each term of the sequence of polynomials P(1), P(2), ... at x=1, x=2 and x=10, respectively. [Edited and corrected by Peter Munn, Aug 12 2022]
REFERENCES
Joseph J. Rotman, The Theory of Groups: An Introduction, 2nd ed. Boston: Allyn and Bacon, Inc. 1973. Page 9, problem 1.26.
LINKS
Sam Alexander, Post to sci.math. [Broken link]
PROG
(PARI) a(n) = my(f = factor(n)); sum(k=1, #f~, f[k, 2]*n^(primepi(f[k, 1])-1)); \\ Michel Marcus, Nov 01 2016
CROSSREFS
KEYWORD
easy,nonn
AUTHOR
Sam Alexander, Dec 12 2003
EXTENSIONS
Name edited by Peter Munn, Aug 12 2022
STATUS
approved