A335498 a(n) is the least odd number k such that Omega(k) = n and Omega(k+2) = n+1, where Omega(k) is the number of prime factors of k (A001222).

1, 7, 25, 873, 1375, 41875, 903123, 1015623, 49671873, 200921875, 1157734375, 41898828123, 496308203125, 10506958984375, 7739037109375, 382999267578123, 17016876976778523, 46804302197265625, 80713609326109375

Offset

0,2

Links

Table of n, a(n) for n=0..18.

Example

a(3) = 873 because Omega(873) = Omega(3^2*97) = 3, Omega(873+2) = Omega(5^3*7) = 4 and 873 is the smallest such integer.

Mathematica

a[n_] := Block[{ov=0, v=1, k=3}, While[ov != n || v != n+1, ov = v; k += 2; v = PrimeOmega@ k]; k-2]; a /@ Range[0, 6]

Prog

(PARI)
generate(A, B, n, k) = A=max(A, 2^n); (f(m, p, n) = my(list=List()); if(n==1, forprime(q=max(p, ceil(A/m)), B\m, my(t=m*q); if(bigomega(t-2) == k, listput(list, t-2))), forprime(q=p, sqrtnint(B\m, n), list=concat(list, f(m*q, q, n-1)))); list); vecsort(Vec(f(1, 3, n)));
a(n) = my(x=2^n, y=2*x); while(1, my(v=generate(x, y, n+1, n)); if(#v >= 1, return(v[1])); x=y+1; y=2*x); \\ Daniel Suteu, Jul 08 2023

Crossrefs

Cf. A001222, A322300, A335496.

Sequence in context: A300527 A214593 A342584 * A012490 A354478 A157702

Adjacent sequences: A335495 A335496 A335497 * A335499 A335500 A335501

Keyword

nonn,more

Author

Giovanni Resta, Jun 11 2020

Extensions

a(12)-a(18) from Daniel Suteu, Jul 08 2023

Status

approved