A051027 a(n) = sigma(sigma(n)) = sum of the divisors of the sum of the divisors of n.

1, 4, 7, 8, 12, 28, 15, 24, 14, 39, 28, 56, 24, 60, 60, 32, 39, 56, 42, 96, 63, 91, 60, 168, 32, 96, 90, 120, 72, 195, 63, 104, 124, 120, 124, 112, 60, 168, 120, 234, 96, 252, 84, 224, 168, 195, 124, 224, 80, 128, 195, 171, 120, 360, 195, 360, 186, 234, 168, 480, 96

Offset

1,2

References

József Sándor, On the composition of some arithmetic functions, Studia Univ. Babeș-Bolyai, Vol. 34, No. 1 (1989), pp. 7-14.

József Sándor and Borislav Crstici, Handbook of Number theory II, Kluwer Academic Publishers, 2004, Chapter 1, p. 39.

Links

T. D. Noe, Table of n, a(n) for n=1..5000

Formula

a(n) = A000203(A000203(n)). - Zak Seidov, Aug 29 2012

a(p) = sigma(p+1) = A000203(p+1), for p prime. - Wesley Ivan Hurt, Feb 14 2014

a(n) = 2*n iff n = 2^q with M_(q+1) = 2^(q+1) - 1 is a Mersenne prime, hence iff n = 2^q with q in A090748. - Bernard Schott, Aug 08 2019

a(n) >= 2*n for even n, with equality only when n = 2^k and 2^(k+1) - 1 is prime (Sándor, 1989). - Amiram Eldar, Mar 09 2021

Example

a(2) = 4 because sigma(2)=1+2=3 and sigma(3)=1+3=4. - Zak Seidov, Aug 29 2012

Maple

with(numtheory): [seq(sigma(sigma(n)), n=1..100)];

Mathematica

DivisorSigma[1, DivisorSigma[1, Range[100]]] (* Zak Seidov, Aug 29 2012 *)

Prog

(PARI) a(n)=sigma(sigma(n)); \\ Joerg Arndt, Feb 16 2014
(Python)
from sympy import divisor_sigma as sigma
def a(n): return sigma(sigma(n))
print([a(n) for n in range(1, 62)]) # Michael S. Branicky, Dec 05 2021

Crossrefs

Cf. A000203.

Sequence in context: A310934 A310935 A353804 * A353802 A291402 A328792

Adjacent sequences: A051024 A051025 A051026 * A051028 A051029 A051030

Keyword

easy,nice,nonn,look

Author

Judson Neer

Status

approved