%I #25 Feb 19 2018 12:10:03

%S 1,5,13,37,73,673,1993,15013,49681,239233,1065601,8524807,68198461,

%T 545587687,1704961513,7811750017

%N 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 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 A019269(a(n)) = n and A019269(m) != n for m < a(n). [_Reinhard Zumkeller_, Apr 12 2012]

%D Peter Giblin, "Primes and Programming - an Introduction to Number Theory with Computation", page 118.

%D R. K. Guy, "Unsolved Problems in Number Theory", section B41.

%t 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 (Haskell)

%o import Data.List (elemIndex)

%o import Data.Maybe (fromJust)

%o a019268 = (+ 1) . fromJust . (`elemIndex` a019269_list)

%o -- _Reinhard Zumkeller_, Apr 12 2012

%Y Cf. A005113, A082449.

%K nonn,nice,more

%O 0,2

%A _Jud McCranie_

%E More terms from _Jud McCranie_, Jan 15 1997

%E Initial element corrected by _Reinhard Zumkeller_, Apr 12 2012