A132435 Composite integers n with two prime factors nearly equidistant from the integer part of the square root of n.

4, 6, 9, 10, 14, 22, 25, 35, 49, 55, 65, 77, 85, 91, 119, 121, 143, 169, 187, 209, 221, 247, 253, 289, 299, 319, 323, 361, 377, 391, 407, 437, 493, 527, 529, 551, 589, 629, 667, 697, 703, 713, 841, 851, 899, 943, 961, 989, 1073, 1081, 1147, 1189

Offset: 1

Author

Andrew S. Plewe, Nov 13 2007

Keywords

• nonn

Comments

An integer n is included if, for some value y >= 0: n = A007918(A000196(n) + y) * A007918(A000196(n) - y) Or: n = nextprime(sqrtint(n) + y) * nextprime(sqrtint(n) - y) Where "nextprime(x)" is the smallest prime number >= to x and "sqrtint(z)" is the integer part of the square root of z.

Has many terms in common with A078972. - Bill McEachen, Dec 24 2020

Examples

			25 = nextprime(5 + 0) * nextprime(5 - 0) = 5 * 5 = 25
35 = nextprime(5 + 1) * nextprime(5 - 1) = 7 * 5 = 35
119 = nextprime(10 + 4) * nextprime(10 - 4) = 17 * 7 = 119
		

Links

• Michel Marcus, Table of n, a(n) for n = 1..3406

Crossrefs

Cf. A007918, A000196, A078972.

Programs

PARI

bal(x,y) = nextprime(sqrtint(x)+y) * nextprime(sqrtint(x)-y);
findbal(x) = local(z,y); z=sqrtint(x); while( 0<=z, y=bal(x,z); if(y==x, print1(x", ");break;); z--;);
for (n=1,1200, findbal(n));