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

1,7

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

Mathematica

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

Crossrefs

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

Sequence in context: A211992 A182937 A340035 * A206921 A327402 A123529

Adjacent sequences: A185144 A185145 A185146 * A185148 A185149 A185150

Keyword

nonn

Author

T. D. Noe, Mar 18 2011

Status

approved