A122261 Characteristic function of numbers having only factors that are Pierpont primes.

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

Offset: 1

Author

Reinhard Zumkeller, Aug 29 2006

Keywords

• nonn
• mult

Examples

			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.
		

Links

• Antti Karttunen, Table of n, a(n) for n = 1..12289
• Eric Weisstein's World of Mathematics, Pierpont Prime
• Index entries for characteristic functions

Crossrefs

Cf. A005109, A065333, A122255, A122262 (partial sums).

Characteristic function of A122260.

Programs

Mathematica

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 *)

PARI

A065333(n) = ((3^valuation(n, 3)<Charles R Greathouse IV, Aug 21 2011
A122261(n) = factorback(apply(p -> A065333(p-1), (factor(n)[, 1]))); \\ Antti Karttunen, Aug 22 2017

Formula

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.

Extensions

An unnecessary part removed from the formula and the Example section added by Antti Karttunen, Aug 22 2017