1,6

a(A007947(n)) = a(n);

A006093 and A001747 give record values and where they occur:

A006093(n)=a(A001747(n+1)) for n>1.

a(n) = 1 iff n is a prime power: a(A000961(n))=1;

a(n) = 2 iff n has exactly 2 and 3 as prime factors:

a(A033845(n))=2;

a(n) = 3 iff n is in A143202;

a(n) = 4 iff n has exactly 2 and 5 as prime factors:

a(A033846(n))=4;

a(n) = 5 iff n is in A143203;

a(n) = 6 iff n is in A143204;

a(n) = 7 iff n is in A143205;

a(n) <> A006512(k)+1 for k>1.

R. Zumkeller, Table of n, a(n) for n = 1..10000

Index entries for primes, gaps between

a(n) = f(n,1,1) where f(n,q,y) = if n=1 then y else if q=1 then f(n/p,p,1)) else f(n/p,p,y*(p-q+1)) with p = A020639(n) = smallest prime factor of n.

a(86) = a(43*2) = 43-2+1 = 42;

a(138) = a(23*3*2) = (23-3+1)*(3-2+1) = 42;

a(172) = a(43*2*2) = (43-2+1)*(2-2+1) = 42;

a(182) = a(13*7*2) = (13-7+1)*(7-2+1) = 42;

a(276) = a(23*3*2*2) = (23-3+1)*(3-2+1)*(2-2+1) = 42;

a(330) = a(11*5*3*2) = (11-5+1)*(5-3+1)*(3-2+1) = 42.

Cf. A109313.

Sequence in context: A157113 A139320 A118106 this_sequence A158298 A112331 A133910

Adjacent sequences: A143198 A143199 A143200 this_sequence A143202 A143203 A143204

nonn

Reinhard Zumkeller (reinhard.zumkeller(AT)gmail.com), Aug 12 2008