A174857 The minimum distance k > 0 such that A020639(n+k) = A020639(n).

2, 6, 2, 20, 2, 42, 2, 6, 2, 110, 2, 156, 2, 6, 2, 272, 2, 342, 2, 6, 2, 506, 2, 10, 2, 6, 2, 812, 2, 930, 2, 6, 2, 20, 2, 1332, 2, 6, 2, 1640, 2, 1806, 2, 6, 2, 2162, 2, 28, 2, 6, 2, 2756, 2, 10, 2, 6, 2, 3422, 2, 3660, 2, 6, 2, 20, 2, 4422, 2, 6, 2, 4970, 2, 5256, 2, 6, 2, 14, 2, 6162

Offset: 2

Author

Vladimir Shevelev, Mar 31 2010

Keywords

• nonn

Comments

The sequence has the same records as A002618.

Links

• Antti Karttunen, Table of n, a(n) for n = 2..16385

Crossrefs

Cf. A020639, A002618, A036689, A174869.

Programs

Maple

A174857 := proc(n) local k,aref ; aref := A020639(n) ; for k from 1 do if A020639(n+k) = aref then return k; end if; end do: end proc:
seq(A174857(n),n=2..80) ; # R. J. Mathar, Dec 07 2010

Mathematica

Block[{s = Array[FactorInteger[#][[1, 1]] &, 10^4]}, Array[If[EvenQ[#], 2, Block[{k = 1, n = s[[#]]}, While[n != s[[# + k]], k++; If[# + k > Length[s], AppendTo[s, FactorInteger[# + k][[1, 1]] ]] ]; k]] &, 78, 2]] (* Michael De Vlieger, Apr 06 2021 *)

PARI

A020639(n) = if(1==n, n, factor(n)[1, 1]);
A174857(n) = if(isprime(n), (n-1)*n, my(spf=A020639(n)); for(k=1,oo,if(A020639(n+k)==spf,return(k)))); \\ Antti Karttunen, Apr 06 2021

Formula

If n is even, then a(n) = 2.

If n = 3k and A020639(k) >= 3, then a(n) = 6.

If n is prime, then a(n) = A036689(n).