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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.
0
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, 121, 12, 24, 36, 48, 13, 169, 14, 28, 98, 15, 45, 75, 16, 32, 64, 128, 256, 17, 289, 18, 36, 54, 162, 19, 361, 20, 40, 80, 100, 21, 63, 147, 22, 44, 242, 23, 529
OFFSET
1,2
COMMENTS
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.
Conjecture: row n includes n^2 if and only if n is a power of a prime number (A000961).
EXAMPLE
Triangle begins:
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, 121;
12, 24, 36, 48;
13, 169;
14, 28, 98;
15, 45, 75;
16, 32, 64, 128, 256;
...
PROG
(PARI) row(n) = select(x->((numdiv(x)<2*numdiv(n)) && !(x % n)), [1..n^2]); \\ Michel Marcus, Jan 26 2021
CROSSREFS
Columns k=1..2 give: A000027, A285109 (for n>=2).
Last elements of rows give A225004.
Sequence in context: A155749 A198931 A344425 * A293779 A063379 A000463
KEYWORD
nonn,tabf
AUTHOR
J. Lowell, Jan 25 2021
STATUS
approved