%I #32 Feb 05 2021 00:50:12

%S 1,2,4,3,9,4,8,16,5,25,6,12,18,7,49,8,16,32,64,9,27,81,10,20,50,11,

%T 121,12,24,36,48,13,169,14,28,98,15,45,75,16,32,64,128,256,17,289,18,

%U 36,54,162,19,361,20,40,80,100,21,63,147,22,44,242,23,529

%N Irregular triangle in which the n-th row consists of all multiples of n that have fewer than twice as many divisors as n.

%C If n has d divisors, n has an infinite number of multiples with exactly 2d divisors, but only a finite number of multiples with fewer than 2d divisors.

%C Conjecture: row n includes n^2 if and only if n is a power of a prime number (A000961).

%e Triangle begins:

%e 1;

%e 2, 4;

%e 3, 9;

%e 4, 8, 16;

%e 5, 25;

%e 6, 12, 18;

%e 7, 49;

%e 8, 16, 32, 64;

%e 9, 27, 81;

%e 10, 20, 50;

%e 11, 121;

%e 12, 24, 36, 48;

%e 13, 169;

%e 14, 28, 98;

%e 15, 45, 75;

%e 16, 32, 64, 128, 256;

%e ...

%o (PARI) row(n) = select(x->((numdiv(x)<2*numdiv(n)) && !(x % n)), [1..n^2]); \\ _Michel Marcus_, Jan 26 2021

%Y Columns k=1..2 give: A000027, A285109 (for n>=2).

%Y Last elements of rows give A225004.

%Y Cf. A000005, A000961.

%K nonn,tabf

%O 1,2

%A _J. Lowell_, Jan 25 2021