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A050703 Numbers that when added to the sum of their prime factors (with multiplicity) become prime. 34
6, 10, 12, 14, 15, 20, 21, 26, 33, 34, 35, 38, 44, 46, 48, 51, 55, 57, 58, 65, 68, 74, 85, 86, 90, 93, 96, 111, 112, 116, 118, 123, 135, 141, 143, 145, 155, 158, 161, 166, 177, 178, 185, 188, 194, 201, 203, 205, 206, 208, 209, 210, 212, 215, 221, 224, 225, 252 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,1
COMMENTS
No term of this sequence can be prime, since for a prime p, A075254(p)=2*p, hence not prime. - Michel Marcus, Jul 24 2015
From Robert Israel, Jul 24 2015: (Start)
Similarly, no term of the sequence can be a prime power.
Contains 2*n for n in A023208 and 3*n for n in A023213. (End)
LINKS
FORMULA
{n: A075254(n) in A000040}. - R. J. Mathar, Jul 27 2015
EXAMPLE
252 = 2*2*3*3*7; 252 + (2 + 2 + 3 + 3 + 7) = 252 + 17 = 269, which is prime.
MAPLE
filter:= n ->isprime(convert(map(convert, ifactors(n)[2], `*`), `+`)+n):
select(filter, [$1..1000]); # Robert Israel, Jul 24 2015
MATHEMATICA
upto=300; Rest[Select[Complement[Range[upto], Prime[Range[ PrimePi[upto]]]], PrimeQ[#+ Total[Times@@@FactorInteger[#]]]&]] (* Harvey P. Dale, Apr 20 2011 *)
Select[Range[500], PrimeQ[# + Total [Times @@@ FactorInteger[#]] && PrimeOmega[#] > 1] &] (* K. D. Bajpai, Sep 12 2014 *)
PROG
(PARI) sopfr(n)=my(f=factor(n)); sum(i=1, #f[, 1], f[i, 1]*f[i, 2])
is(n)=!isprime(n)&&isprime(n+sopfr(n)) \\ Charles R Greathouse IV, Jul 19 2011
CROSSREFS
Sequence in context: A080363 A289558 A082300 * A361126 A330397 A135711
KEYWORD
nonn,nice
AUTHOR
Patrick De Geest, Aug 15 1999
EXTENSIONS
Name clarified by Michel Marcus, Jul 24 2015
STATUS
approved

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Last modified June 21 07:08 EDT 2024. Contains 373540 sequences. (Running on oeis4.)