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A122261
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Characteristic function of numbers having only factors that are Pierpont primes.
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4
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1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 0, 1, 1, 1, 1, 1, 0, 1, 0, 1, 0, 1, 1, 1, 1, 1, 1, 1, 0, 1, 0, 0, 1, 0, 0, 1, 1, 1, 1, 1, 0, 1, 0, 1, 1, 0, 0, 1, 0, 0, 1, 1, 1, 0, 0, 1, 0, 1, 0, 1, 1, 1, 1, 1, 0, 1, 0, 1, 1, 0, 0, 1, 1, 0, 0, 0, 0, 1, 1, 0, 0, 0, 1, 1, 1, 1, 0, 1, 0, 1, 0, 1, 1
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OFFSET
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1,1
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LINKS
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Antti Karttunen, Table of n, a(n) for n = 1..12289
Eric Weisstein's World of Mathematics, Pierpont Prime
Index entries for characteristic functions
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FORMULA
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Multiplicative with a(p) = A065333(p-1), for p prime.
a(n) = if n=1 then 0 else A122262(n) - A122262(n-1).
a(A122260(n)) = 1.
a(n) = A122255(n) for n < 25.
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EXAMPLE
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For n = 11 = 11^1, 11 is not a Pierpoint prime because 11-1 = 10 = 2*5 has a prime factor larger than 3, thus a(11) = 0.
For n = 25 = 5^2, 5 is a Pierpoint prime as 5-1 = 4 = 2^2 does not have any prime factors larger than 3, thus a(25) = 1.
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MATHEMATICA
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Block[{nn = 105, s}, s = Select[Sort@ Flatten@ Table[2^i*3^j + 1, {i, 0, Log2@ nn}, {j, 0, Log[3, nn/2^i]}] , PrimeQ]; Table[Boole[n == 1] + Boole@ AllTrue[FactorInteger[n][[All, 1]], MemberQ[s, #] &], {n, nn}]] (* Michael De Vlieger, Aug 23 2017, after Robert G. Wilson v at A005109 *)
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PROG
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(PARI)
A065333(n) = ((3^valuation(n, 3)<<valuation(n, 2))==n); \\ This function from Charles R Greathouse IV, Aug 21 2011
A122261(n) = factorback(apply(p -> A065333(p-1), (factor(n)[, 1]))); \\ Antti Karttunen, Aug 22 2017
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CROSSREFS
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Cf. A005109, A065333, A122255, A122262 (partial sums).
Characteristic function of A122260.
Sequence in context: A225595 A228813 A122255 * A014922 A014988 A015076
Adjacent sequences: A122258 A122259 A122260 * A122262 A122263 A122264
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KEYWORD
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nonn,mult
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AUTHOR
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Reinhard Zumkeller, Aug 29 2006
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EXTENSIONS
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An unnecessary part removed from the formula and the Example section added by Antti Karttunen, Aug 22 2017
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STATUS
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approved
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