A271606 - OEIS

%I #8 Aug 05 2019 06:37:29

%S 1,0,1,1,1,1,1,1,1,1,0,2,1,1,1,0,1,2,0,1,1,0,0,3,0,1,0,2,0,1,2,2,1,0,

%T 0,1,0,1,1,1,0,3,0,1,0,0,0,3,0,2,0,0,0,2,0,2,1,0,0,3,0,1,1,0,1,0,0,1,

%U 0,0,0,5,1,1,0,0,0,1,0,2,0,1,0,3,1,0,0,0,0,3,2,0,1,0,0,4,0,2,0,0

%N Number of numbers k such that sigma_e(k) = n for some e > 0.

%C We can't just define this as number of pairs k, e  with e > 0 that have sigma_e(k) = n, because sigma_e(1) = 1 for all e.

%H Amiram Eldar, <a href="/A271606/b271606.txt">Table of n, a(n) for n = 1..10000</a>

%e a(28) = 2 because 28 = sigma_1(12) = 1+2+3+4+6+12 and also 28 = sigma_3(3) = 1^3+3^3.

%o (PARI) alist(n)=my(r=vector(n),s);r[1]=1;for(k=2,n,e=1;while((s=sigma(k,e))<=n,r[s]++;e++));r

%Y Cf. A054973, A109974.

%K nonn

%O 1,12

%A _Franklin T. Adams-Watters_, Apr 10 2016