A086711 Primes p such that A001414(p-1) = A001414(p+1), where A001414 = sum of primes dividing n (with repetition).

11, 17, 31, 251, 1429, 3041, 16561, 16927, 53299, 56897, 89783, 95089, 213599, 282977, 345547, 432587, 592223, 763457, 906949, 915799, 1050449, 1058389, 1485017, 1577341, 1678399, 1780253, 1855549, 2131687, 2374289, 2658259

Offset

1,1

Comments

Conjecture: sequence is infinite.

Links

Charles R Greathouse IV, Table of n, a(n) for n = 1..1280

Example

a(3)=31 because it is prime and 30=2*3*5, 32=2^5 and 2+3+5 = 2+2+2+2+2 = 10.

Mathematica

spdn[n_]:=Total[Flatten[Table[#[[1]], #[[2]]]&/@FactorInteger[n]]]; Select[Prime[Range[200000]], spdn[#-1]==spdn[#+1]&] (* Harvey P. Dale, Nov 25 2025 *)

Crossrefs

Cf. A001414, A190680.

Sequence in context: A165667 A339180 A392974 * A039514 A098797 A271999

Adjacent sequences: A086708 A086709 A086710 * A086712 A086713 A086714

Keyword

nonn

Author

Jason Earls, Jul 28 2003

Status

approved