

A093035


Number of triples (d1,d2,d3) where each element is a divisor of n and d1 + d2 + d3 <= n.


0



0, 0, 1, 4, 1, 17, 1, 20, 8, 20, 1, 103, 1, 20, 27, 54, 1, 109, 1, 112, 27, 20, 1, 315, 8, 20, 27, 112, 1, 315, 1, 112, 27, 20, 27, 481, 1, 20, 27, 324, 1, 321, 1, 112, 125, 20, 1, 695, 8, 112, 27, 112, 1, 321, 27, 324, 27, 20, 1, 1285, 1, 20
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OFFSET

1,4


COMMENTS

It appears that a(n) depends on both parity of n and its prime signature. For instance a(odd prime)=1, a(even semiprime)=20, a(odd semiprime)=27, a(odd prime cube)=27, a(odd prime fourth power)=64. Maybe it is possible to find a formula for a(n). Similar sequences with pairs, quadruples, ... instead of triples can be envisioned.  Michel Marcus, Aug 21 2013


LINKS

Table of n, a(n) for n=1..62.


EXAMPLE

a(9) = 8 because the divisors of 9 are {1,3,9} making the valid triples (1,1,1), (1,1,3), (1,3,1), (1,3,3), (3,1,1), (3,1,3), (3,3,1), (3,3,3).


PROG

(PARI) a(n) = {nb = 0; d = divisors(n); for (i = 1, #d, for (j = 1, #d, for (k = 1, #d, if (d[i]+d[j]+d[k] <= n, nb++); ); ); ); nb; } \\ Michel Marcus, Aug 21 2013


CROSSREFS

Sequence in context: A111661 A072651 A209411 * A126791 A052179 A171589
Adjacent sequences: A093032 A093033 A093034 * A093036 A093037 A093038


KEYWORD

easy,nonn


AUTHOR

Jonathan A. Cohen (cohenj02(AT)tartarus.uwa.edu.au), May 08 2004


STATUS

approved



