login
Numbers k such that A113177(k) and A276085(k) are both even, where A113177 and A276085 are fully additive with a(p) = Fibonacci(p) and a(p) = p#/p, respectively.
6

%I #7 Jun 29 2024 11:18:02

%S 1,3,4,9,12,16,25,27,35,36,48,49,55,64,65,75,77,81,85,91,95,100,105,

%T 108,115,119,121,133,140,143,144,145,147,155,161,165,169,185,187,192,

%U 195,196,203,205,209,215,217,220,221,225,231,235,243,247,253,255,256,259,260,265,273,285,287,289,295,299,300,301,305

%N Numbers k such that A113177(k) and A276085(k) are both even, where A113177 and A276085 are fully additive with a(p) = Fibonacci(p) and a(p) = p#/p, respectively.

%C Numbers whose 2-adic valuation (A007814) is even, and the number of the prime factors (with multiplicity, A001222) and the 3-adic valuation (A007949) have the same parity.

%C A multiplicative semigroup: if m and n are in the sequence, then so is m*n.

%H Antti Karttunen, <a href="/A374114/b374114.txt">Table of n, a(n) for n = 1..12000</a>

%o (PARI) isA374114 = A374113;

%Y Intersection of A003159 and A373586.

%Y Indices of even terms in A374112.

%Y Cf. A001222, A007814, A007949, A113177, A276085, A374113 (characteristic function), A374115 (complement).

%K nonn

%O 1,2

%A _Antti Karttunen_, Jun 29 2024