A176292 Numbers k such that the prime factorizations of composite(k) and composite(k+1) have the same number of primes (including multiplicities).

1, 4, 7, 10, 12, 15, 17, 18, 21, 22, 25, 28, 29, 40, 47, 53, 61, 62, 64, 68, 69, 72, 85, 87, 90, 91, 93, 100, 102, 106, 107, 110, 112, 114, 116, 120, 125, 130, 131, 132, 133, 136, 151, 154, 155, 158, 165, 166, 169, 170, 179, 181, 190, 191, 198, 212, 221, 222, 223

Offset: 1

Author

Juri-Stepan Gerasimov, Apr 14 2010

Keywords

• nonn

Links

• Harvey P. Dale, Table of n, a(n) for n = 1..1000

Crossrefs

Cf. A045920, A045939.

Programs

Maple

A001222 := proc(n) numtheory[bigomega](n) ; end proc:
A002808 := proc(n) if n = 1 then return 4; else for a from procname(n-1)+1 do if not isprime(a) then return a; end if; end do; end if; end proc:
for n from 1 to 400 do if A001222(A002808(n)) = A001222(A002808(n+1)) then printf("%d,",n) ; end if; end do: # R. J. Mathar, Apr 20 2010

Mathematica

SequencePosition[PrimeOmega/@Select[Range[300],CompositeQ],{x_,x_}][[;;,1]] (* Harvey P. Dale, Jun 21 2023 *)

Formula

A001222(A002808(a(n))) = A001222(A002808(a(n)+1)).

Extensions

Corrected (86 replaced with 87, 89 removed, many terms after 92 replaced) by R. J. Mathar, Apr 20 2010