

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.


2



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
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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

Table of n, a(n) for n=1..38.
Kevin Brown and Charles Vanden Eynden, Pseudoaliquot Sequences, Solution to Problem 10323, The American Mathematical Monthly, Volume 103, No. 8 (1996), pp. 697698.
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

Cf. A001615, A002025, A033845 (Dedekind psi perfect numbers), A323327, A323328, A323330.
Sequence in context: A250873 A205091 A038854 * A182371 A252258 A038677
Adjacent sequences: A323326 A323327 A323328 * A323330 A323331 A323332


KEYWORD

nonn


AUTHOR

Amiram Eldar, Jan 11 2019


STATUS

approved



