A379238 a(n) = 1 if A003961(n)-sigma(n) is prime, otherwise 0, where A003961 is fully multiplicative with a(prime(i)) = prime(i+1), and sigma is the sum of divisors function.

0, 0, 0, 1, 0, 1, 1, 0, 0, 1, 0, 1, 1, 0, 1, 0, 0, 0, 1, 0, 1, 1, 1, 0, 0, 0, 0, 1, 0, 0, 1, 0, 1, 1, 1, 0, 1, 0, 1, 0, 0, 0, 1, 0, 1, 0, 1, 1, 0, 0, 1, 0, 1, 0, 1, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 1, 1, 0, 1, 0, 0, 1, 1, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 1, 0, 1, 1, 1, 0, 1, 0, 0, 1, 0, 0

Offset

1

Links

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

Index entries for characteristic functions.

Index entries for sequences related to prime indices in the factorization of n.

Index entries for sequences related to sigma(n).

Formula

a(1) = a(2) = 0, and for n > 2, a(n) = A010051(A286385(n)).

Prog

(PARI)
A003961(n) = { my(f = factor(n)); for(i=1, #f~, f[i, 1] = nextprime(f[i, 1]+1)); factorback(f); };
A379238(n) = isprime(A003961(n)-sigma(n));

Crossrefs

Characteristic function of A379239.

Cf. A000203, A003961, A010051, A286385.

Cf. also A349167.

Sequence in context: A341612 A252742 A066247 * A151774 A095792 A288381

Adjacent sequences: A379233 A379235 A379237 * A379239 A379240 A379241

Keyword

nonn,new

Author

Antti Karttunen, Dec 23 2024

Status

approved