A233819 -id:A233819 - cp's OEIS frontend

A093035 Number of triples (d1,d2,d3) where each element is a divisor of n and d1 + d2 + d3 <= n.

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

Offset: 1

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

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

There's more to the story above. It seems that a(A233819(n)) gives the largest possible value per prime signature. Some prime signatures may have more than two possible values for a(n). - David A. Corneth, May 19 2020

			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).

Antti Karttunen, Table of n, a(n) for n = 1..16384
Antti Karttunen, Data supplement: n, a(n) computed for n = 1..65537

Cf. A233819.

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

A327328 a(n) is the smallest positive integer divisible by exactly n nonpowers of 2.

Original entry on oeis.org

1, 3, 6, 12, 18, 45, 30, 105, 72, 60, 90, 315, 120, 3645, 210, 180, 450, 1575, 480, 2835, 360, 420, 630, 3465, 900, 720, 7290, 1620, 840, 14175, 1440, 10395, 1800, 1260, 3150, 1680, 3240, 1937102445, 5670, 14580, 3600, 127575, 3360, 2066715, 2520, 3780, 6930

Offset: 0

Omar E. Pol, Sep 20 2019

nonn

Terms are of the form A233819(m) * 2^k for some m > 0, k >= 0. - David A. Corneth, Nov 25 2019

David A. Corneth, Table of n, a(n) for n = 0..1000

Cf. A057716, A233819, A326987, A326989.

ispp(x) = my(p); (x == 1) || (isprimepower(x, &p) && (p==2));
nbdiv(k) = #select(x->(!ispp(x)), divisors(k));
a(n) = my(k=1); while (nbdiv(k) != n, k++); k; \\ Michel Marcus, Nov 25 2019

a(n) = for(i = 1, oo, if(numdiv(i) - valuation(i, 2) - 1 == n, return(i))) \\ David A. Corneth, Nov 25 2019

a(13)-a(36), a(38)-a(46) from Jon E. Schoenfield, Nov 22 2019

a(37) from Jon E. Schoenfield and David A. Corneth, Nov 25 2019

cp's OEIS Frontend

A093035 Number of triples (d1,d2,d3) where each element is a divisor of n and d1 + d2 + d3 <= n.

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A327328 a(n) is the smallest positive integer divisible by exactly n nonpowers of 2.

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