|
|
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
Similarly, no term of the sequence can be a prime power.
|
|
LINKS
|
|
|
FORMULA
|
|
|
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):
|
|
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])
|
|
CROSSREFS
|
|
|
KEYWORD
|
nonn,nice
|
|
AUTHOR
|
|
|
EXTENSIONS
|
|
|
STATUS
|
approved
|
|
|
|