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A182318
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List of positive integers whose prime tower factorization, as defined in comments, does not contain the prime 2.
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5
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1, 3, 5, 7, 11, 13, 15, 17, 19, 21, 23, 27, 29, 31, 33, 35, 37, 39, 41, 43, 47, 51, 53, 55, 57, 59, 61, 65, 67, 69, 71, 73, 77, 79, 83, 85, 87, 89, 91, 93, 95, 97, 101, 103, 105, 107, 109, 111, 113, 115, 119, 123, 125, 127, 129, 131, 133, 135, 137, 139, 141, 143, 145, 149
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OFFSET
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1,2
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COMMENTS
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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.
As an alternative definition, let I(n) be the indicator function for the set of positive integers whose prime tower factorization does not contain a 2. Then I(n) is the multiplicative function satisfying I(p^k) = I(k) for p prime not equal to 2, and I(2^k) = 0.
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LINKS
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Table of n, a(n) for n=1..64.
Patrick Devlin and Edinah Gnang, Primes Appearing in Prime Tower Factorization, arXiv:1204.5251v1 [math.NT]
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MAPLE
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# The integer n is in this sequence if and only if
# conatinsPrimeInTower(2, n) returns false
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:
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CROSSREFS
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Sequence in context: A175679 A088828 A182662 * A056911 A152955 A210719
Adjacent sequences: A182315 A182316 A182317 * A182319 A182320 A182321
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KEYWORD
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nonn
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AUTHOR
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Patrick Devlin, Apr 24 2012
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STATUS
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approved
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