A342259 Numbers k such that omega(k-1) = omega(k)-1 and omega(k+1) = omega(k)+1, where omega(m) is the number of distinct primes dividing m, A001221(m).

65, 104, 129, 164, 194, 272, 284, 314, 344, 384, 398, 464, 524, 608, 614, 626, 662, 692, 734, 758, 824, 968, 1025, 1094, 1172, 1238, 1280, 1304, 1364, 1424, 1448, 1454, 1532, 1544, 1595, 1658, 1664, 1682, 1724, 1754, 1832, 1868, 1869, 1934, 1952, 2000, 2001, 2012

Offset: 1

Author

Hugo Pfoertner, Mar 07 2021

Keywords

• nonn

Examples

			a(1)=65: 64=2^6 (1 distinct prime 2), 65=5*13 (2 distinct primes 5 and 13), 66=2*3*11 (3 distinct primes 2, 3, and 11).
		

Links

• Hugo Pfoertner, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A001221, A342258.

Programs

Mathematica

seq[nmax_] := Module[{om}, om[n_] := om[n] = PrimeNu[n]; Select[Range[2, nmax], om[# - 1] == om[#] - 1 && om[# + 1] == om[#] + 1 &]]; seq[2500] (* Amiram Eldar, Sep 19 2024 *)

PARI

for(n=3,2100,my(om=omega(n));if(omega(n-1)==om-1&&omega(n+1)==om+1,print1(n,", ")))