A174869 a(n) is 0 if n is a power of 2, otherwise the smallest k > 0 such that A006530(n+k) < A006530(n).

0, 0, 1, 0, 1, 2, 1, 0, 7, 2, 1, 4, 1, 1, 1, 0, 1, 14, 1, 4, 3, 2, 1, 8, 2, 1, 5, 2, 1, 2, 1, 0, 2, 1, 1, 28, 1, 1, 1, 8, 1, 3, 1, 1, 3, 2, 1, 16, 1, 4, 1, 2, 1, 10, 1, 4, 3, 2, 1, 4, 1, 1, 1, 0, 1, 4, 1, 2, 1, 2, 1, 56, 1, 1, 6, 1, 3, 2, 1, 1, 47, 2, 1, 6, 3, 1, 1, 2, 1, 6, 5, 3, 2, 1, 1, 32, 1, 2, 1, 8, 1, 2, 1

Offset: 1

Author

Vladimir Shevelev, Mar 31 2010

Keywords

• nonn

Comments

a(n)=1 if the index n is an odd prime.

Links

• Antti Karttunen, Table of n, a(n) for n = 1..8192
• Antti Karttunen, Data supplement: n, a(n) computed for n = 1..65537

Crossrefs

Cf. A006530, A103667, A023503, A023509, A174857, A020639, A002618, A036689.

Programs

Maple

A006530 := proc(n) option remember; if n = 1 then 1; else max(op(numtheory[factorset](n)) ) ; end if; end proc:
A174869 := proc(n) if n <= 2 then 0; else gpf := A006530(n) ; if gpf = 2 then 0; else for k from 1 do if A006530(n+k) < gpf then return k; end if; end do: end if; end if; end proc:
seq(A174869(n),n=1..120) ; # R. J. Mathar, Aug 10 2010

Mathematica

Block[{s = Array[FactorInteger[#][[-1, 1]] &, 120]}, Array[If[IntegerQ@ Log2[#], 0, Block[{k = 1, n = s[[#]]}, While[n <= s[[# + k]], k++; If[# + k > Length[s], AppendTo[s, FactorInteger[# + k][[-1, 1]] ]] ]; k]] &, 102, 2]] (* Michael De Vlieger, Apr 06 2021 *)

PARI

A006530(n) = if(n>1, vecmax(factor(n)[, 1]), 1);
A174869(n) = if(!bitand(n,n-1), 0, my(gpf=A006530(n)); for(k=1,oo,if(A006530(n+k)Antti Karttunen, Apr 06 2021

Extensions

More terms from R. J. Mathar, Aug 10 2010