OFFSET
1,1
COMMENTS
This set is the complement of A182318.
The prime tower factorization of a number can be recursively defined as follows:
(0) The prime tower factorization of 1 is itself
(1) To find the prime tower factorization of an integer n>1, let n = p1^e1 * p2^e2 * ... * pk^ek be the usual prime factorization of n. Then the prime tower factorization is given by p1^(f1) * p2^(f2) * ... * pk^(fk), where fi is the prime tower factorization of ei.
LINKS
Amiram Eldar, Table of n, a(n) for n = 1..10000
Patrick Devlin and Edinah Gnang, Primes Appearing in Prime Tower Factorization, arXiv:1204.5251 [math.NT], 2012-2014.
MAPLE
# The integer n is in this sequence if and only if
# conatinsPrimeInTower(2, n) returns true
conatinsPrimeInTower:=proc(q, n) local i, L, currentExponent; option remember;
if n <= 1 then return false: end if;
if type(n/q, integer) then return true: end if;
L := ifactors(n)[2];
for i to nops(L) do currentExponent := L[i][2];
if containsPrimeInTower(q, currentExponent) then return true: end if
end do;
return false:
end proc:
MATHEMATICA
Select[Range[120], MemberQ[Flatten@ FixedPoint[Map[If[PrimeQ@ Last@# || Last@# == 1, #, {First@#, FactorInteger@Last@#}]&, #, {Depth@# - 2}]&, FactorInteger@#], 2]&] (* Jean-François Alcover, Mar 27 2018, using Michael De Vlieger's program for A182318 )
CROSSREFS
KEYWORD
nonn
AUTHOR
Patrick Devlin, Apr 25 2012
STATUS
approved