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(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
KEYWORD
AUTHOR
STATUS
approved