A230578 - OEIS

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A230578

Smallest number larger than 1 such that multiplying n-th highly composite number by a(n) will give a highly composite number.

2, 2, 3, 2, 2, 2, 5, 5, 2, 2, 2, 3, 2, 7, 2, 2, 3, 2, 2, 2, 2, 3, 11, 2, 2, 11, 11, 2, 2, 2, 2, 3, 2, 2, 13, 13, 13, 2, 2, 2, 2, 3, 2, 2, 5, 2, 2, 2, 3, 17, 2, 17, 2, 17, 2, 2, 5, 2, 2, 2, 3, 19, 2, 2, 2, 3, 2, 2, 5, 19, 2, 2, 2, 3, 5, 2, 2, 2, 2, 23, 7, 2, 2

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OFFSET

1,1

COMMENTS

Conjecture: all a(n) are prime numbers.

This conjecture is false: a(643) = 6 is not prime. - Alois P. Heinz, Oct 23 2013

LINKS

Table of n, a(n) for n=1..83.

EXAMPLE

a(3) cannot be 2 because the third highly composite number, 4, when multiplied by 2, yields 8, which is not a highly composite number.

CROSSREFS

Cf. A002182.