

A048138


a(n) = number of m such that sum of proper divisors of m (A001065(m)) is n.


24



0, 1, 1, 0, 2, 1, 2, 1, 1, 1, 1, 2, 2, 2, 2, 2, 1, 2, 2, 3, 2, 2, 1, 3, 1, 2, 1, 2, 1, 5, 2, 3, 1, 3, 1, 4, 1, 1, 3, 4, 2, 5, 2, 3, 2, 3, 1, 6, 2, 4, 0, 3, 2, 6, 1, 5, 1, 3, 1, 6, 2, 3, 3, 6, 1, 6, 1, 2, 1, 5, 1, 8, 3, 4, 3, 5, 1, 7, 1, 6, 1, 4, 1, 8, 1, 5, 0, 5, 2, 9, 2, 4, 1, 4, 0, 9, 1, 3, 2, 6, 1, 8, 2, 7, 4
(list;
graph;
refs;
listen;
history;
text;
internal format)



OFFSET

2,5


COMMENTS

The offset is 2 since there are infinitely many numbers (all the primes) for which A001065 = 1.
The graph of this sequence, shifted by 1, looks similar to that of A061358, which counts Goldbach partitions of n.  T. D. Noe, Dec 05 2008
For n > 2, a(n) <= A000009(n) as all divisor lists must have distinct values.  Roderick MacPhee, Sep 13 2016


REFERENCES

Carl Pomerance, The first function and its iterates, pp. 125138 in Connections in Discrete Mathematics, ed. S. Butler et al., Cambridge, 2018.


LINKS

T. D. Noe, Table of n, a(n) for n = 2..10000


EXAMPLE

a(6) = 2 since 6 is the sum of the proper divisors of 6 and 25.


MAPLE

with(numtheory): for n from 2 to 150 do count := 0: for m from 1 to n^2 do if sigma(m)  m = n then count := count+1 fi: od: printf(`%d, `, count): od:


PROG

(PARI) list(n)=my(v=vector(n1), k); for(m=4, n^2, k=sigma(m)m; if(k>1 & k<=n, v[k1]++)); v \\ Charles R Greathouse IV, Apr 21 2011


CROSSREFS

Cf. A001065, A005114, A064440, A238895, A238896 (records).
Sequence in context: A269975 A308069 A161895 * A165022 A030338 A231148
Adjacent sequences: A048135 A048136 A048137 * A048139 A048140 A048141


KEYWORD

easy,nonn


AUTHOR

Naohiro Nomoto


EXTENSIONS

More terms from James A. Sellers, Feb 19 2001


STATUS

approved



