A203182 Primes p such that A008472(p-1) = A008472(p+1), where A008472 = sum of distinct primes dividing n.

3, 18913, 24733, 29633, 32429, 42719, 45751, 46103, 61409, 117991, 149351, 171529, 174019, 176017, 223099, 294893, 326369, 363691, 421727, 423503, 434237, 472631, 658579, 678077, 686423, 706841, 735901, 770059, 771629, 906949, 936827, 937571, 1073447, 1256029

Offset: 1

Author

Michel Lagneau, Dec 30 2011

Keywords

• nonn

Comments

Conjecture: the sequence is infinite.

Examples

			18913 is in the sequence because:
sum of the distinct prime divisors of 18912 = 2+3+197 = 202;
sum of the distinct prime divisors of 18914 = 2+7+193 = 202.
		

Links

• Donovan Johnson, Table of n, a(n) for n = 1..2000

Crossrefs

Cf. A008472, A190680, A086711.

Programs

Maple

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:

Mathematica

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