

A019268


Let Dedekind's psi(m) = product of (p+1)p^(e1) 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.


4



1, 5, 13, 37, 73, 673, 1993, 15013, 49681, 239233, 1065601, 8524807, 68198461, 545587687, 1704961513, 7811750017
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OFFSET

0,2


COMMENTS

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 ErdősSelfridge classification of primes).
A019269(a(n)) = n and A019269(m) != n for m < a(n). [Reinhard Zumkeller, Apr 12 2012]


REFERENCES

Peter Giblin, "Primes and Programming  an Introduction to Number Theory with Computation", page 118.
R. K. Guy, "Unsolved Problems in Number Theory", section B41.


LINKS

Table of n, a(n) for n=0..15.


MATHEMATICA

psi[m_] := ({pp, ee} = FactorInteger[m] // Transpose; If[Max[pp] == 3, m, Times @@ (pp+1)*Times @@ (pp^(ee1))]); 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}] (* JeanFrançois Alcover, Feb 19 2018 *)


PROG

(Haskell)
import Data.List (elemIndex)
import Data.Maybe (fromJust)
a019268 = (+ 1) . fromJust . (`elemIndex` a019269_list)
 Reinhard Zumkeller, Apr 12 2012


CROSSREFS

Cf. A005113, A082449.
Sequence in context: A089523 A058507 A111057 * A083413 A232879 A269803
Adjacent sequences: A019265 A019266 A019267 * A019269 A019270 A019271


KEYWORD

nonn,nice,more


AUTHOR

Jud McCranie


EXTENSIONS

More terms from Jud McCranie, Jan 15 1997
Initial element corrected by Reinhard Zumkeller, Apr 12 2012


STATUS

approved



