

A054973


Number of numbers whose divisors sum to n.


30



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



OFFSET

1,12


COMMENTS

a(n) = frequency of values n in A000203(m), where A000203(m) = sum of divisors of m. a(n) >= 1 for such n that A175192(n) = 1, a(n) >= 1 if A000203(m) = n for any m. a(n) = 0 for such n that A175192(n) = 0, a(n) = 0 if A000203(m) = n has no solution.  Jaroslav Krizek, Mar 01 2010
First occurrence of k: 2, 1, 12, 24, 96, 72, ..., = A007368.  Robert G. Wilson v, May 14 2014


LINKS

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


EXAMPLE

a(12)=2 since 11 has factors 1 and 11 with 1+11=12 and 6 has factors 1, 2, 3 and 6 with 1+2+3+6=12.


MATHEMATICA

nn = 105; t = Table[0, {nn}]; k = 1; While[k < 6 nn^(3/2)/Pi^2, d = DivisorSigma[1, k]; If[d < nn + 1, t[[d]]++]; k++]; t (* Robert G. Wilson v, May 14 2014 *)


PROG

(PARI) a(n)=v = vector(0); for (i = 1, n, if (sigma(i) == n, v = concat(v, i)); ); #v; \\ Michel Marcus, Oct 22 2013
(PARI) a(n)=sum(k=1, n, sigma(k)==n) \\ Charles R Greathouse IV, Nov 12 2013
(PARI) first(n)=my(v=vector(n), t); for(k=1, n, t=sigma(n); if(t<=n, v[t]++)); v \\ Charles R Greathouse IV, Mar 08 2017


CROSSREFS

Cf. A000203, A002191, A007609.
Sequence in context: A089053 A214979 A068462 * A030351 A257994 A188921
Adjacent sequences: A054970 A054971 A054972 * A054974 A054975 A054976


KEYWORD

nonn


AUTHOR

Henry Bottomley, May 16 2000


STATUS

approved



