cp's OEIS Frontend

A353356 Numbers k for which A353328(k) > A353329(k). Positions of 1's in A353354.

%I A353356 #14 Mar 22 2025 19:02:12
%S A353356 2,5,10,11,16,17,22,23,30,31,34,40,41,46,47,54,55,59,62,66,67,70,73,
%T A353356 80,82,83,85,88,94,97,102,103,109,115,118,127,128,130,134,135,136,137,
%U A353356 138,146,149,154,155,157,165,166,167,176,179,184,186,187,190,191,194,197,205,206,211,218,227,233,235,238,240,241
%N A353356 Numbers k for which A353328(k) > A353329(k). Positions of 1's in A353354.
%C A353356 For any term k present here, A003961(k) is present in A353357.
%H A353356 <a href="/index/Pri#prime_indices">Index entries for sequences computed from indices in prime factorization</a>
%F A353356 {a(n) : n >= 1} = {m : tau(m) * A048675(m) == 2 (mod 3)}, where tau is the number of divisors function, A000005.
%o A353356 (PARI)
%o A353356 A332823(n) = { my(f = factor(n),u=(sum(k=1, #f~, f[k, 2]*2^primepi(f[k, 1]))/2)%3); if(2==u,-1,u); };
%o A353356 A353354(n) = sumdiv(n,d,A332823(d));
%o A353356 isA353356(n) = (0<A353354(n));
%o A353356 (PARI)
%o A353356 A048675(n) = { my(f = factor(n)); sum(k=1, #f~, f[k, 2]*2^primepi(f[k, 1]))/2; };
%o A353356 isA353356(n) = (2==((numdiv(n)*A048675(n))%3));
%Y A353356 Cf. A000005, A003961, A048675, A332823, A353328, A353329, A353354, A353355, A353357.
%K A353356 nonn
%O A353356 1,1
%A A353356 _Antti Karttunen_ and _Peter Munn_, Apr 15 2022