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A340896 Irregular triangle in which the n-th row consists of all multiples of n that have fewer than twice as many divisors as n.

%I A340896 #32 Feb 05 2021 00:50:12
%S A340896 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 A340896 121,12,24,36,48,13,169,14,28,98,15,45,75,16,32,64,128,256,17,289,18,
%U A340896 36,54,162,19,361,20,40,80,100,21,63,147,22,44,242,23,529
%N A340896 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 A340896 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 A340896 Conjecture: row n includes n^2 if and only if n is a power of a prime number (A000961).
%e A340896 Triangle begins:
%e A340896    1;
%e A340896    2,   4;
%e A340896    3,   9;
%e A340896    4,   8, 16;
%e A340896    5,  25;
%e A340896    6,  12, 18;
%e A340896    7,  49;
%e A340896    8,  16, 32,  64;
%e A340896    9,  27, 81;
%e A340896   10,  20, 50;
%e A340896   11, 121;
%e A340896   12,  24, 36,  48;
%e A340896   13, 169;
%e A340896   14,  28, 98;
%e A340896   15,  45, 75;
%e A340896   16,  32, 64, 128, 256;
%e A340896   ...
%o A340896 (PARI) row(n) = select(x->((numdiv(x)<2*numdiv(n)) && !(x % n)), [1..n^2]); \\ _Michel Marcus_, Jan 26 2021
%Y A340896 Columns k=1..2 give: A000027, A285109 (for n>=2).
%Y A340896 Last elements of rows give A225004.
%Y A340896 Cf. A000005, A000961.
%K A340896 nonn,tabf
%O A340896 1,2
%A A340896 _J. Lowell_, Jan 25 2021