cp's OEIS Frontend

A019268 Let Dedekind's psi(m) = product of (p+1)p^(e-1) for primes p, where p^e is a factor of m. Iterating psi(m) eventually results in a number of form 2^a*3^b. a(n) is the smallest number that requires n steps to reach such a number.

%I A019268 #25 Feb 19 2018 12:10:03
%S A019268 1,5,13,37,73,673,1993,15013,49681,239233,1065601,8524807,68198461,
%T A019268 545587687,1704961513,7811750017
%N A019268 Let Dedekind's psi(m) = product of (p+1)p^(e-1) for primes p, where p^e is a factor of m. Iterating psi(m) eventually results in a number of form 2^a*3^b. a(n) is the smallest number that requires n steps to reach such a number.
%C A019268 There is a remarkable and unexplained agreement: if 5 is dropped from the list, 2, 673, 1993 and 239233 are replaced by 1, 1021, 29173 and 532801, the result is sequence A005113 (least prime of class n+, according to the Erdős-Selfridge classification of primes).
%C A019268 A019269(a(n)) = n and A019269(m) != n for m < a(n). [_Reinhard Zumkeller_, Apr 12 2012]
%D A019268 Peter Giblin, "Primes and Programming - an Introduction to Number Theory with Computation", page 118.
%D A019268 R. K. Guy, "Unsolved Problems in Number Theory", section B41.
%t A019268 psi[m_] := ({pp, ee} = FactorInteger[m] // Transpose; If[Max[pp] == 3, m, Times @@ (pp+1)*Times @@ (pp^(ee-1))]); a[0] = 1; a[1] = 5; a[n_] := a[n] = For[k = a[n - 1] (* assuming monotony *), True, k++, If[Length @ FixedPointList[psi, k] == n+2, Return[k]]]; Table[Print["a(", n, ") = ", a[n]]; a[n], {n, 0, 10}] (* _Jean-François Alcover_, Feb 19 2018 *)
%o A019268 (Haskell)
%o A019268 import Data.List (elemIndex)
%o A019268 import Data.Maybe (fromJust)
%o A019268 a019268 = (+ 1) . fromJust . (`elemIndex` a019269_list)
%o A019268 -- _Reinhard Zumkeller_, Apr 12 2012
%Y A019268 Cf. A005113, A082449.
%K A019268 nonn,nice,more
%O A019268 0,2
%A A019268 _Jud McCranie_
%E A019268 More terms from _Jud McCranie_, Jan 15 1997
%E A019268 Initial element corrected by _Reinhard Zumkeller_, Apr 12 2012