A271606 Number of numbers k such that sigma_e(k) = n for some e > 0.

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, 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, 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

Offset: 1

Author

Franklin T. Adams-Watters, Apr 10 2016

Keywords

• nonn

Comments

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.

Examples

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

Links

• Amiram Eldar, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A054973, A109974.

Programs

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