A203182 - OEIS

%I #11 Sep 22 2013 14:51:13

%S 3,18913,24733,29633,32429,42719,45751,46103,61409,117991,149351,

%T 171529,174019,176017,223099,294893,326369,363691,421727,423503,

%U 434237,472631,658579,678077,686423,706841,735901,770059,771629,906949,936827,937571,1073447,1256029

%N Primes p such that A008472(p-1) = A008472(p+1), where A008472 = sum of distinct primes dividing n.

%C Conjecture: the sequence is infinite.

%H Donovan Johnson, <a href="/A203182/b203182.txt">Table of n, a(n) for n = 1..2000</a>

%e 18913 is in the sequence because:

%e sum of the distinct prime divisors of 18912 = 2+3+197 = 202;

%e sum of the distinct prime divisors of 18914 = 2+7+193 = 202.

%p with(numtheory):for n from 1 to 100000 do:p:=ithprime(n):p1:=p-1: p2:=p+1:t1:=ifactors(p1)[2]; t11 := sum(t1[i][1], i=1..nops(t1)):t2:=ifactors(p2)[2]; t22 := sum(t2[i][1], i=1..nops(t2)):if t11=t22 then printf(`%d, `,p):else fi:od:

%t Select[Prime[Range[100000]],Total[Transpose[FactorInteger[#-1]][[1]]] == Total[Transpose[FactorInteger[#+1]][[1]]]&] (* _Harvey P. Dale_, Sep 22 2013 *)

%Y Cf. A008472, A190680, A086711.

%K nonn

%O 1,1

%A _Michel Lagneau_, Dec 30 2011