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%I #11 Feb 07 2019 02:12:29
%S 2,3,7,23,131,313,353,397,887,1307,1439,1783,2003,2027,2069,2111,2593,
%T 2777,3541,4111,4201,4889,5653,5897,6421,6823,8353,8447,9721,9749,
%U 11159,11483,12011,12073,12251,13313,14323,14431,15083,15131,15887,17029
%N Primes p such that the p-th semiprime divided by the sum of the digits of p is a prime.
%H Harvey P. Dale, <a href="/A176706/b176706.txt">Table of n, a(n) for n = 1..500</a>
%e 131 is a term because the 131st semiprime is 415, the sum of the digits of 131 is 5, and 415/5 = 83, which is prime.
%p isA001358 := proc(n) numtheory[bigomega](n) = 2 ; end proc:
%p A001358 := proc(n) option remember ; if n = 1 then return 4 ; else for a from procname(n-1)+1 do if isA001358(a) then return a; end if; end do; end if; end proc:
%p A007953 := proc(n) add(d,d=convert(n,base,10)) ; end proc:
%p isA176706 := proc(n) if isprime(n) then r := A001358(n)/A007953(n) ; if type(r,'integer') then isprime(r) ; else false; end if; else false; end if; end proc:
%p for n from 1 to 2000 do p := ithprime(n) ; if isA176706(p) then printf("%d,",p) ; end if; end do: # _R. J. Mathar_, Apr 24 2010
%t Module[{semis=Select[Range[100000],PrimeOmega[#]==2&]},Select[ Prime[ Range[ PrimePi[ Length[semis]]]], PrimeQ[semis[[#]]/ Total[ IntegerDigits[ #]]]&]] (* _Harvey P. Dale_, May 10 2014 *)
%Y Cf. A001358, A007605, A106350.
%K nonn,base
%O 1,1
%A _Juri-Stepan Gerasimov_, Apr 24 2010
%E Keyword:base added, sequence extended by _R. J. Mathar_, Apr 24 2010
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