

A323329


Lesser of amicable pair m < n defined by t(n) = m and t(m) = n where t(n) = psi(n)  n and psi(n) = A001615(n) is the Dedekind psi function.


4



1330, 2660, 3850, 5320, 6650, 7700, 10640, 11270, 13300, 14950, 15400, 18550, 19250, 21280, 22540, 26600, 29900, 30800, 33250, 37100, 38500, 42560, 45080, 53200, 59800, 61600, 66500, 73370, 74200, 74750, 77000, 78890, 85120, 90160, 92750, 96250, 106400, 119600
(list;
graph;
refs;
listen;
history;
text;
internal format)



OFFSET

1,1


COMMENTS

t(n) = psi(n)  n is the sum of aliquot divisors of n, d, such that n/d is squarefree. Penney & Pomerance proposed a problem to show that the "pseudoaliquot" sequence related to this function is unbounded. This sequence lists number with pseudoaliquot sequence of cycle 2. The sequence that is analogous to perfect numbers is A033845.


LINKS

David E. Penney and Carl Pomerance, Problem 10323, The American Mathematical Monthly, Volume 100, No. 7 (1993), p. 688.


MATHEMATICA

psi[n_] := n*Times@@(1+1/Transpose[FactorInteger[n]][[1]]); t[n_]:= psi[n]  n; s={}; Do[n=t[m]; If[n>m && t[n]==m, AppendTo[s, m]], {m, 1, 120000}]; s


CROSSREFS



KEYWORD

nonn


AUTHOR



STATUS

approved



