A135591 a(1)=1; for n > 1, a(n) is number of earlier terms equal to number of proper divisors of n.

1, 1, 2, 1, 3, 1, 4, 1, 1, 1, 7, 0, 7, 1, 1, 1, 10, 0, 10, 0, 1, 1, 12, 2, 2, 1, 1, 0, 14, 2, 14, 0, 1, 1, 1, 0, 17, 1, 1, 2, 19, 2, 19, 0, 0, 1, 20, 0, 6, 0, 1, 0, 21, 2, 1, 2, 1, 1, 24, 0, 24, 1, 0, 1, 1, 2, 27, 0, 1, 2, 28, 0, 28, 1, 0, 0, 1, 2, 30, 0, 1, 1, 32, 0, 1, 1, 1, 2, 35, 0, 1, 0, 1, 1, 1, 0, 39

Offset: 1

Author

Katarzyna Matylla, Feb 25 2008

Keywords

• nonn

Comments

Similar to A125087, but instead of exponents, we use number of proper divisors.

Examples

			a(12)=0 because 12 has 5 proper divisors (1, 2, 3, 4 and 6) and there is no 5 in a(1), a(2), ..., a(11).
		

Links

• Katarzyna Matylla, Table of n, a(n) for n = 1..1000

Crossrefs

Cf. A032741, A125087.

Programs

Mathematica

s={1};Do[AppendTo[s,Count[s,DivisorSigma[0,n]-1]],{n,2,97}];s (* James C. McMahon, Apr 16 2025 *)

Maxima

max:1000; f:makelist(0,i,1,max); apr:makelist(0, i, 0, max); f[1]:1; apr[2]:1; for n:2 through max do block(f[n]:apr[divsum(n,0)], apr[f[n]+1]:apr[f[n]+1]+1);