A356742 Numbers k such that k and k+2 both have exactly 4 divisors.

6, 8, 33, 55, 85, 91, 93, 123, 141, 143, 159, 183, 185, 201, 203, 213, 215, 217, 219, 235, 247, 265, 299, 301, 303, 319, 321, 327, 339, 341, 391, 393, 411, 413, 415, 445, 451, 469, 471, 515, 517, 533, 535, 543, 551, 579, 581, 589, 633, 667, 669, 679, 685, 687, 695, 697

Offset: 1

Author

Jianing Song, Aug 25 2022

Keywords

• nonn

Comments

6 and 8 are the only even terms: one of the two consecutive even numbers is divisible by 4, and the only multiple of 4 with exactly 4 divisors is 8.

Examples

			341 is a term since 341 and 343 both have 4 divisors.
		

Links

• Jianing Song, Table of n, a(n) for n = 1..10000

Crossrefs

Numbers k such that k and k+2 both have exactly m divisors: A001359 (m=2), this sequence (m=4), A356743 (m=6), A356744 (m=8).

Cf. also A039832 (numbers k such that k and k+1 both have exactly 4 divisors).

Programs

Mathematica

SequencePosition[DivisorSigma[0,Range[700]],{4,,4}][[All,1]] (* _Harvey P. Dale, Oct 07 2022 *)

PARI

isA356742(n) = numdiv(n)==4 && numdiv(n+2)==4