|
%I #45 Dec 05 2021 17:28:33
%S 1,4,7,8,12,28,15,24,14,39,28,56,24,60,60,32,39,56,42,96,63,91,60,168,
%T 32,96,90,120,72,195,63,104,124,120,124,112,60,168,120,234,96,252,84,
%U 224,168,195,124,224,80,128,195,171,120,360,195,360,186,234,168,480,96
%N a(n) = sigma(sigma(n)) = sum of the divisors of the sum of the divisors of n.
%D József Sándor, On the composition of some arithmetic functions, Studia Univ. Babeș-Bolyai, Vol. 34, No. 1 (1989), pp. 7-14.
%D József Sándor and Borislav Crstici, Handbook of Number theory II, Kluwer Academic Publishers, 2004, Chapter 1, p. 39.
%H T. D. Noe, <a href="/A051027/b051027.txt">Table of n, a(n) for n=1..5000</a>
%F a(n) = A000203(A000203(n)). - _Zak Seidov_, Aug 29 2012
%F a(p) = sigma(p+1) = A000203(p+1), for p prime. - _Wesley Ivan Hurt_, Feb 14 2014
%F 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
%F 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
%e a(2) = 4 because sigma(2)=1+2=3 and sigma(3)=1+3=4. - _Zak Seidov_, Aug 29 2012
%p with(numtheory): [seq(sigma(sigma(n)), n=1..100)];
%t DivisorSigma[1,DivisorSigma[1,Range[100]]] (* _Zak Seidov_, Aug 29 2012 *)
%o (PARI) a(n)=sigma(sigma(n)); \\ _Joerg Arndt_, Feb 16 2014
%o (Python)
%o from sympy import divisor_sigma as sigma
%o def a(n): return sigma(sigma(n))
%o print([a(n) for n in range(1, 62)]) # _Michael S. Branicky_, Dec 05 2021
%Y Cf. A000203.
%K easy,nice,nonn,look
%O 1,2
%A _Judson Neer_
|
