A114985 Numbers whose sum of distinct prime factors is semiprime.

14, 21, 26, 28, 30, 33, 38, 46, 52, 56, 57, 60, 62, 63, 69, 70, 74, 76, 85, 90, 92, 93, 94, 98, 99, 102, 104, 105, 106, 112, 120, 124, 129, 133, 134, 140, 145, 147, 148, 150, 152, 166, 171, 174, 177, 178, 180, 182, 184, 188, 189, 190, 195, 196, 204, 205, 207, 208

Offset

1,1

Comments

This is the semiprime analog of A114522 "numbers n such that sum of distinct prime divisors of n is prime." See also A110893 "numbers with a semiprime number of prime divisors (counted with multiplicity)."

Links

Table of n, a(n) for n=1..58.

Formula

{k such that A008472(k) is an element of A001358}. {k such that sopf(k) is an element of A001358}. {k = Product(Prime(j)^e_j) such that Sum(Prime(j)) is in A001358}.

Example

a(1) = 14 because 14 = 2 * 7 and 2 + 7 = 9 = 3^2 is semiprime.
a(2) = 21 because 21 = 3 * 7 and 3 + 7 = 10 = 2 * 5 is semiprime.
a(3) = 26 because 26 = 2 * 13 and 2 + 13 = 15 = 3 * 5 is semiprime.
a(4) = 28 because 28 = 2^2 * 7 and 2 + 7 = 9 = 3^2 is semiprime.
a(5) = 30 because 30 = 2 * 3 * 5 and 2 + 3 + 5 = 10 = 2 * 5 is semiprime.
a(6) = 33 because 33 = 3 * 11 and 3 + 11 = 14 = 2 * 7 is semiprime.
a(7) = 38 because 38 = 2 * 19 and 2 + 19 = 21 = 3 * 7 is semiprime.

Maple

with(numtheory): a:=proc(n) local A, s, B: A:=factorset(n): s:=sum(A[j], j=1..nops(A)): B:=factorset(s): if nops(B)=2 and B[1]*B[2]=s or nops(B)=1 and B[1]^2=s then n else fi end: seq(a(n), n=2..250); # Emeric Deutsch, Mar 07 2006

Mathematica

Select[Range[250], PrimeOmega[Total[Transpose[FactorInteger[#]][[1]]]]==2&] (* Harvey P. Dale, May 06 2013 *)

Prog

(PARI) is(n)=bigomega(vecsum(factor(n)[, 1]))==2 \\ Charles R Greathouse IV, Sep 14 2015

Crossrefs

Cf. A001358, A008472, A110893, A114522.

Sequence in context: A129497 A255742 A093994 * A344703 A001944 A024803

Adjacent sequences: A114982 A114983 A114984 * A114986 A114987 A114988

Keyword

easy,nonn

Author

Jonathan Vos Post, Feb 22 2006

Extensions

Corrected and extended by Emeric Deutsch, Mar 07 2006

Status

approved