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A048138 a(n) = number of m such that sum of proper divisors of m (A001065(m)) is n. 20
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

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

CROSSREFS

Cf. A001065, A005114, A064440, A238895, A238896 (records).

Sequence in context: A269974 A269975 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

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Last modified June 28 21:30 EDT 2017. Contains 288840 sequences.