A336851 a(n) = sigma(A003961(n)) - A003961(n), where A003961 is a prime shift towards larger primes, sigma is the sum of divisors.

0, 1, 1, 4, 1, 9, 1, 13, 6, 11, 1, 33, 1, 15, 13, 40, 1, 49, 1, 41, 17, 17, 1, 105, 8, 21, 31, 57, 1, 87, 1, 121, 19, 23, 19, 178, 1, 27, 23, 131, 1, 123, 1, 65, 73, 33, 1, 321, 12, 81, 25, 81, 1, 249, 21, 183, 29, 35, 1, 309, 1, 41, 97, 364, 25, 141, 1, 89, 35, 153, 1, 565, 1, 45, 97, 105, 25, 177, 1, 401, 156, 47

Offset

1,4

Comments

Even terms occur on square n, odd terms on nonsquare n.

Numbers k such that a(k) = 2^e for e >= 1, are: 4, 25, 841, 12769, 66896041, etc., i.e., terms of A073715 squared.

Links

Antti Karttunen, Table of n, a(n) for n = 1..16384

Antti Karttunen, Data supplement: n, a(n) computed for n = 1..65537

Index entries for sequences computed from indices in prime factorization

Index entries for sequences related to sigma(n)

Formula

a(n) = A003973(n) - A003961(n) = A000203(A003961(n)) - A003961(n).

a(n) = A001065(A003961(n)).

a(n) = A336852(n) - A286385(n).

Prog

(PARI)
A003961(n) = { my(f = factor(n)); for(i=1, #f~, f[i, 1] = nextprime(f[i, 1]+1)); factorback(f); };
A336851(n) = (sigma(A003961(n)) - A003961(n));

Crossrefs

Cf. A000203, A001065, A003961, A003973, A073715, A252748, A286385, A326042, A336852.

Cf. A336850 [= gcd(a(n),A003961(n))].

Sequence in context: A208508 A123726 A323600 * A138675 A274091 A080103

Adjacent sequences: A336848 A336849 A336850 * A336852 A336853 A336854

Keyword

nonn

Author

Antti Karttunen, Aug 05 2020

Extensions

Comments edited by Antti Karttunen, Jul 03 2023

Status

approved