A283235 Triangle read by rows: n-th row gives the numbers of primes p such that p*prime(k) <= prime(n)^2, k=1..n.

1, 2, 2, 5, 4, 3, 9, 6, 4, 4, 17, 12, 9, 7, 5, 23, 16, 11, 9, 6, 6, 34, 24, 16, 13, 9, 8, 7, 41, 30, 20, 15, 11, 9, 8, 8, 56, 40, 27, 21, 15, 12, 11, 9, 9, 81, 59, 39, 30, 21, 18, 15, 14, 11, 10

Offset: 1

Author

Zak Seidov, Mar 03 2017

Keywords

• nonn
• tabl

Comments

Sequence is related to A128301 = indices of squares (of primes) in the semiprimes.

Examples

			Triangle begins:
   1;
   2,  2;
   5,  4,  3;
   9,  6,  4,  4;
  17, 12,  9,  7,  5;
  23, 16, 11,  9,  6,  6;
  34, 24, 16, 13,  9,  8,  7;
  41, 30, 20, 15, 11,  9,  8,  8;
  56, 40, 27, 21, 15, 12, 11,  9,  9;
  81, 59, 39, 30, 21, 18, 15, 14, 11, 10;
  ...
		

Crossrefs

Cf. A128301, A348836 (1st column).

Programs

Mathematica

Table[PrimePi[Prime[n]^2/Prime[k]],{n,10},{k,n}]//Flatten

PARI

row(n) = my(p=prime(n)); vector(n, k, primepi(p^2/prime(k))); \\ Michel Marcus, Nov 01 2021