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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 (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 "pseudo-aliquot" sequence related to this function is unbounded. This sequence lists number with pseudo-aliquot 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, Pseudo-aliquot Sequences, Solution to Problem 10323, The American Mathematical Monthly, Volume 103, No. 8 (1996), pp. 697-698.

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

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Last modified April 26 12:00 EDT 2019. Contains 322472 sequences. (Running on oeis4.)