A381104 a(n) is the number of prime factors with exponent 1 in the prime factorization of the n-th superabundant number.
0, 1, 0, 2, 1, 1, 0, 1, 2, 2, 1, 2, 1, 1, 3, 2, 3, 2, 2, 2, 2, 1, 3, 3, 3, 3, 2, 3, 2, 3, 4, 4, 4, 3, 4, 3, 4, 3, 3, 5, 4, 5, 4, 5, 4, 4, 6, 4, 4, 5, 6, 5, 6, 5, 5, 5, 5, 5, 5, 4, 6, 6, 6, 6, 6, 6, 5, 6, 5, 5, 5, 7, 5, 7, 7, 7, 7, 6, 7, 6, 6, 6, 8, 6, 8, 8, 8, 8, 7, 8, 7, 7, 7, 7, 9, 7, 9, 7, 7, 9, 8, 9, 8, 8, 8
Offset: 1
Keywords
Examples
For n=8 the 8th superabundant number is 48 = 2^4*3^1. Only one prime factor appears with exponent 1 so a(8) = 1.
Links
- Alois P. Heinz, Table of n, a(n) for n = 1..2000
- L. Alaoglu and P. Erdős, On highly composite and similar numbers, Trans. Amer. Math. Soc., 56 (1944), 448-469. Errata.
- Kevin Broughan, Equivalents of the Riemann Hypothesis, Vol. 1: Arithmetic Equivalents, Cambridge University Press, 2017.
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