A355943 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.

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, 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, 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

Offset

1

Links

Antti Karttunen, Table of n, a(n) for n = 1..100000

Index entries for characteristic functions

Index entries for sequences computed from indices in prime factorization

Index entries for sequences related to sigma(n)

Formula

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

a(n) = A000035(n) * A361465(n) = A000035(n) * A361466(A064989(n)). - Antti Karttunen, Mar 20 2023

Prog

(PARI)
A003961(n) = { my(f = factor(n)); for (i=1, #f~, f[i, 1] = nextprime(f[i, 1]+1)); factorback(f); };
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)};
A348942(n) = { my(u=A326042(n)); (u / gcd(n, u)); };
A355943(n) = ((n%2)&&!(A064989(n)%A064989(sigma(n))));

Crossrefs

Characteristic function of A348943.

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

Cf. also A355946.

Sequence in context: A373371 A379651 A321692 * A102242 A005369 A278169

Adjacent sequences: A355940 A355941 A355942 * A355944 A355945 A355946

Keyword

nonn

Author

Antti Karttunen, Jul 23 2022

Status

approved