A338261 The least number of the form 2^i*3^j (i, j >= 0) which can be represented as a product of the greatest number of distinct positive integers in exactly n ways.

1, 12, 72, 96, 3456, 576, 1536, 55296, 864, 9216, 56623104, 6912, 1769472, 62208, 34359738368, 746496, 110592, 93312, 3145728, 82944, 15925248, 1327104, 32614907904, 995328, 1679616, 3538944, 42467328, 1207959552, 18874368, 382205952, 286654464, 22463437455746924544, 8707129344, 1855425871872, 13060694016, 14495514624, 2717908992, 270826551115776, 17915904, 226492416

Offset

1,2

Comments

The numbers 2^i*3^j and 2^j*3^i have the same number of ways to represent them as a product of the greatest number of distinct divisors. Therefore each term of the sequence is a number of the form 2^i*3^j for which i>=j>=0.

Links

Table of n, a(n) for n=1..40.

Example

a(5) = 2^7*3^3 = 3456 because 3456 = 1*2*3*4*6*24 = 1*2*3*4*8*18 = 1*2*3*4*9*16 = 1*2*3*6*8*12 = 1*2*4*6*8*9 and each number of the form 2^i*3^j (i, j >= 0) less than 3456 does not have 5 representations as a product of the greatest number of distinct positive integers.

Crossrefs

Cf. A338159.

Sequence in context: A362518 A209447 A219302 * A101523 A340302 A143698

Adjacent sequences: A338258 A338259 A338260 * A338262 A338263 A338264

Keyword

nonn

Author

Dmitry Khomovsky, Oct 19 2020

Status

approved