A355943 - OEIS

%I #12 May 11 2023 16:57:05

%S 1,0,1,0,0,0,1,0,0,0,0,0,0,0,1,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,1,0,1,0,

%T 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,

%U 1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,1,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1

%N a(n) = 1 if n is odd and A064989(sigma(n)) divides A064989(n), otherwise 0, where A064989 is fully multiplicative with a(2) = 1 and a(p) = prevprime(p) for odd primes p, and sigma is the sum of divisors function.

%H Antti Karttunen, <a href="/A355943/b355943.txt">Table of n, a(n) for n = 1..100000</a>

%H <a href="/index/Ch#char_fns">Index entries for characteristic functions</a>

%H <a href="/index/Pri#prime_indices">Index entries for sequences computed from indices in prime factorization</a>

%H <a href="/index/Si#SIGMAN">Index entries for sequences related to sigma(n)</a>

%F a(n) = A000035(n) * [0 == A064989(n) mod A350073(n)], where [ ] is the Iverson bracket.

%F a(n) = A000035(n) * A361465(n) = A000035(n) * A361466(A064989(n)). - _Antti Karttunen_, Mar 20 2023

%o (PARI)

%o A003961(n) = { my(f = factor(n)); for (i=1, #f~, f[i, 1] = nextprime(f[i, 1]+1)); factorback(f); };

%o A064989(n) = {my(f); f = factor(n); if((n>1 && f[1,1]==2), f[1,2] = 0); for (i=1, #f~, f[i,1] = precprime(f[i,1]-1)); factorback(f)};

%o A348942(n) = { my(u=A326042(n)); (u / gcd(n, u)); };

%o A355943(n) = ((n%2)&&!(A064989(n)%A064989(sigma(n))));

%Y Characteristic function of A348943.

%Y Cf. A000035, A003961, A064989, A326042, A348942, A350073, A361465, A361466.

%Y Cf. also A355946.

%K nonn

%O 1

%A _Antti Karttunen_, Jul 23 2022