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

1,1

Comments

Conjecture: the sequence is infinite.

Links

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

Example

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.

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 *)

Crossrefs

Cf. A008472, A190680, A086711.

Sequence in context: A155180 A364963 A182914 * A128121 A112406 A344681

Adjacent sequences: A203179 A203180 A203181 * A203183 A203184 A203185

Keyword

nonn

Author

Michel Lagneau, Dec 30 2011

Status

approved