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

1,2

Links

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

Formula

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

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 *)

Crossrefs

Cf. A045920, A045939.

Sequence in context: A214641 A178598 A310675 * A050173 A078633 A190008

Adjacent sequences: A176289 A176290 A176291 * A176293 A176294 A176295

Keyword

nonn

Author

Juri-Stepan Gerasimov, Apr 14 2010

Extensions

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

Status

approved