A108609 6-almost primes whose sum of factors is a prime.

96, 224, 360, 416, 486, 504, 600, 608, 792, 810, 992, 1176, 1184, 1224, 1368, 1376, 1400, 1890, 1952, 2040, 2088, 2184, 2232, 2250, 2336, 2528, 2600, 2754, 2760, 2904, 2952, 3080, 3104, 3296, 3384, 3480, 3510, 3640, 3726, 4064, 4158, 4248, 4312, 4392

Offset

1,1

Links

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

Example

96=2*2*2*2*2*3 (6-almost prime) and 2+2+2+2+2+3=13 is a prime.

Mathematica

Select[Range[8000], Last[Plus@@FactorInteger[ # ]]==6&&PrimeQ[Plus@@Times@@ Transpose[FactorInteger[ # ]]]&]
sfp6Q[n_]:=Module[{pf=Flatten[Table[#[[1]], #[[2]]]&/@FactorInteger[n]]}, Length[ pf]==6&&PrimeQ[Total[pf]]]; Select[Range[4400], sfp6Q] (* Harvey P. Dale, Jul 01 2018 *)

Prog

(PARI) is(n)=my(f=factor(n)); sum(i=1, #f~, f[i, 2])==6 && isprime(sum(i=1, #f~, f[i, 1]*f[i, 2])) \\ Charles R Greathouse IV, Oct 11 2013

Crossrefs

Cf. A107707, A108607, A108608 (resp.) 3, 4, 5 (resp.)-almost primes whose sum of factors is a prime.

Sequence in context: A241930 A270435 A110231 * A125511 A124106 A304510

Adjacent sequences: A108606 A108607 A108608 * A108610 A108611 A108612

Keyword

nonn

Author

Zak Seidov, Jun 12 2005

Status

approved