A185147 Number of times each value of the sigma function occurs.

1, 1, 1, 1, 1, 1, 2, 1, 1, 1, 2, 1, 3, 1, 1, 2, 2, 1, 1, 1, 1, 3, 1, 3, 2, 2, 1, 3, 1, 1, 1, 5, 1, 1, 2, 3, 3, 1, 1, 4, 2, 1, 2, 2, 1, 1, 2, 4, 1, 2, 2, 1, 2, 2, 1, 1, 2, 5, 1, 2, 2, 1, 1, 1, 1, 6, 1, 1, 1, 4, 2, 1, 2, 5, 1, 1, 1, 1, 1, 2, 1, 5, 1, 1, 3, 3, 1, 3, 7, 1, 3, 6, 1, 1, 1, 1, 2, 1, 3, 2

Offset: 1

Author

T. D. Noe, Mar 18 2011

Keywords

• nonn

Comments

The possible values of the sigma (sum of divisors) function are in A002191. Value A002191(n) occurs exactly a(n) times. Because sigma(x) >= x+1 (for x>1) with equality only at prime x, we know that for prime p, sigma(p) is the last time p+1 occurs as a value of sigma. This sequence is the same as A054973 without the zero terms.

Links

• T. D. Noe, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A007370 (numbers for which a(n)=1).

Programs

Mathematica

Transpose[Sort[Tally[DivisorSigma[1, Range[Prime[PrimePi[200]]]]]]][[2]]