|
|
A051027
|
|
a(n) = sigma(sigma(n)) = sum of the divisors of the sum of the divisors of n.
|
|
100
|
|
|
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
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
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
|
|
|
FORMULA
|
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))
|
|
CROSSREFS
|
|
|
KEYWORD
|
|
|
AUTHOR
|
|
|
STATUS
|
approved
|
|
|
|