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A182338
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List of positive integers whose prime tower factorization, as defined in comments, contains the prime 3.
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1
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3, 6, 8, 9, 12, 15, 18, 21, 24, 27, 30, 33, 36, 39, 40, 42, 45, 48, 51, 54, 56, 57, 60, 63, 64, 66, 69, 72, 75, 78, 81, 84, 87, 88, 90, 93, 96, 99, 102, 104, 105, 108, 111, 114, 117, 120, 123, 125, 126, 129, 132, 135, 136, 138, 141, 144, 147, 150, 152, 153
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OFFSET
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1,1
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COMMENTS
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This set is the complement of A182337.
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.
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LINKS
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MAPLE
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# The integer n is in this sequence if and only if
# containsPrimeInTower(3, n) returns true
containsPrimeInTower:=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:
select(x-> containsPrimeInTower(3, x), [$1..160])[];
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MATHEMATICA
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indic[1] = 1; indic[n_] := indic[n] = Switch[f = FactorInteger[n], {{3, _}}, 0, {{_, _}}, indic[f[[1, 2]]], _, Times @@ (indic /@ (Power @@@ f))];
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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