A283486 Number of k such that sigma(k) = 2n where sigma(m) = A000203(m) is the sum of the divisors of m.

0, 1, 1, 1, 0, 2, 1, 0, 2, 1, 0, 3, 0, 1, 1, 2, 0, 1, 1, 1, 3, 1, 0, 3, 0, 0, 2, 2, 0, 3, 1, 0, 0, 1, 0, 5, 1, 0, 1, 2, 0, 3, 0, 0, 3, 0, 0, 4, 2, 0, 1, 2, 0, 2, 1, 1, 2, 0, 0, 4, 0, 2, 2, 2, 0, 2, 0, 0, 1, 2, 0, 5, 0, 0, 1, 2, 0, 2, 1, 1, 1, 1, 0, 6, 0, 0, 1, 1, 0, 4, 2, 0, 2, 0, 0, 5

Offset: 1

Author

Juri-Stepan Gerasimov, Mar 08 2017

Keywords

• nonn

Comments

First occurrence of k: 1, 2, 6, 12, 48, 36, 84, ...

Examples

			a(12) = 3 because sigma(14) = 1 + 2 + 7 + 14 = 24, sigma(15) = 1 + 3 + 5 + 15 = 24 and sigma(23) = 1 + 23 = 24.
		

Links

• Charles R Greathouse IV, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A000203, A054973, A060658.

Programs

PARI

first(n)=my(v=vector(n),t);for(k=1,2*n-1, t=sigma(k)/2; if(t<=n && denominator(t)==1, v[t]++)); v \\ Charles R Greathouse IV, Mar 08 2017

Formula

a(n) = A054973(2n) - Michel Marcus, Mar 08 2017.

Extensions

a(96) corrected by Charles R Greathouse IV, Mar 08 2017