cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

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).

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%I A342259 #17 Dec 23 2024 03:00:13
%S A342259 65,104,129,164,194,272,284,314,344,384,398,464,524,608,614,626,662,
%T A342259 692,734,758,824,968,1025,1094,1172,1238,1280,1304,1364,1424,1448,
%U A342259 1454,1532,1544,1595,1658,1664,1682,1724,1754,1832,1868,1869,1934,1952,2000,2001,2012
%N 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).
%H A342259 Hugo Pfoertner, <a href="/A342259/b342259.txt">Table of n, a(n) for n = 1..10000</a>
%e A342259 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).
%t A342259 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 *)
%o A342259 (PARI) for(n=3,2100,my(om=omega(n));if(omega(n-1)==om-1&&omega(n+1)==om+1,print1(n,", ")))
%Y A342259 Cf. A001221, A342258.
%K A342259 nonn
%O A342259 1,1
%A A342259 _Hugo Pfoertner_, Mar 07 2021