

A114985


Numbers whose sum of distinct prime factors is semiprime.


0



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
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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 * A001944 A024803 A004432
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



