A109383 5-almost primes of the form semiprime + 1.

112, 120, 162, 300, 304, 378, 392, 396, 408, 520, 552, 567, 592, 612, 630, 656, 675, 680, 688, 696, 700, 750, 780, 918, 924, 944, 952, 980, 990, 1044, 1100, 1116, 1136, 1140, 1160, 1168, 1170, 1242, 1264, 1272, 1300, 1323, 1352, 1372, 1380, 1386, 1416, 1470

Offset: 1

Author

Jonathan Vos Post, Aug 25 2005

Keywords

• easy
• nonn

Examples

			a(1) = 112 because (3*37)+1 = (2^4) * 7 = 112.
a(2) = 120 because (7*17)+1 = (2^3) * 3 * 5 = 120.
a(3) = 162 because (7*23)+1 = 2 * (3^4) = 162.
		

Links

• Charles R Greathouse IV, Table of n, a(n) for n = 1..10000

Crossrefs

Primes are in A000040. Semiprimes are in A001358. 5-almost primes are in A014614.

Primes of the form semiprime + 1 are in A005385 (safe primes).

Semiprimes of the form semiprime + 1 are in A109373.

3-almost primes of the form semiprime + 1 are in A109067.

4-almost primes of the form semiprime + 1 are in A109287.

5-almost primes of the form semiprime + 1 are in this sequence.

Least n-almost prime of the form semiprime + 1 are in A128665.

Cf. A077065, A079148, A092307.

Programs

Mathematica

f[n_] := Plus @@ Last /@ FactorInteger[n];Select[Range[1500], f[ # ] == 5 && f[ # - 1] == 2 &] (* Ray Chandler, Mar 20 2007 *)

PARI

v=vector(10000);i=0; for(n=1,9e99, if(issemi(n)&bigomega(n+1)==5, v[i++]=n+1;if(i==#v, return))); v \\ Charles R Greathouse IV, Feb 14 2011

Formula

a(n) is in this sequence iff a(n) is in A014614 and (a(n)-1) is in A001358.

Extensions

Extended by Ray Chandler, Mar 20 2007