A391384 Primes p such that p - 1 has exactly as many odd divisors as p + 1.

3, 11, 13, 23, 47, 109, 131, 139, 193, 229, 239, 281, 311, 373, 383, 409, 431, 433, 439, 443, 499, 577, 617, 619, 643, 709, 743, 761, 821, 853, 941, 947, 1031, 1033, 1039, 1069, 1103, 1129, 1163, 1181, 1361, 1373, 1429, 1451, 1489, 1549, 1571, 1579, 1607, 1613, 1627, 1669, 1693

Offset

1,1

Links

Robert Israel, Table of n, a(n) for n = 1..10000

Maple

filter:= proc(n);
  isprime(n) and
   NumberTheory:-tau((n-1)/2^padic:-ordp(n-1, 2))=NumberTheory:-tau((n+1)/2^padic:-ordp(n+1, 2))
end proc:
select(filter, [seq(i, i=3..2000, 2)]); # Robert Israel, May 07 2026

Mathematica

d[n_] := DivisorSigma[0, n/2^IntegerExponent[n, 2]]; seq[lim_] := Select[Prime[Range[lim]], Equal @@ d /@ (# + {-1, 1}) &]; seq[265] (* Amiram Eldar, Feb 16 2026 *)

Prog

(Magma) [p: p in PrimesUpTo(2000) | #Divisors(2*(p-1)) + #Divisors(p+1) eq #Divisors(2*(p+1)) + #Divisors(p-1)];
(PARI) isok(p) = isprime(p) && (sumdivmult(p-1, d, d%2) == sumdivmult(p+1, d, d%2)); \\ Michel Marcus, Feb 21 2026

Crossrefs

Subset of A275418. Superset of A275598.

Cf. A001227.

Cf. A067889.

Sequence in context: A045429 A168164 A296933 * A270543 A213697 A287348

Adjacent sequences: A391381 A391382 A391383 * A391385 A391386 A391387

Keyword

nonn

Author

Juri-Stepan Gerasimov, Feb 15 2026

Status

approved