A126132 - OEIS

%I #24 Apr 21 2023 21:15:58

%S 1,2,1,3,1,5,1,7,3,5,1,12,1,7,3,12,1,12,1,15,3,9,1,23,2,10,4,19,1,19,

%T 1,23,4,12,2,33,1,13,4,31,1,22,1,29,6,15,1,45,1,18,5,32,1,31,2,40,5,

%U 17,1,53,1,19,6,45,2,33,1,41,5,23,1,69,1,22,6,45,2,39,1,59,6,23,1,70,3,24,5

%N a(n) = number of k's, 1<=k<=n, where d(k) is equal to any divisor of n, where d(k) is the number of positive divisors of k.

%H Antti Karttunen, <a href="/A126132/b126132.txt">Table of n, a(n) for n = 1..16384</a>

%F a(n) = Sum_{k=1..n} (1 - ceiling(n/d(k)) + floor(n/d(k))). - _Wesley Ivan Hurt_, Apr 21 2023

%e The number of divisors of the integers 1 through 10 form the sequence 1, 2, 2, 3, 2, 4, 2, 4, 3, 4. The divisors of 10 are 1, 2, 5, 10. The terms of the sequence of the first ten d(k)'s which equal any divisor of 10 are the five terms 1, 2, 2, 2, 2. So a(10) = 5.

%t f[n_] := Length@Select[Table[Length@Divisors[k], {k, n}], MemberQ[Divisors[n], # ] &];Table[f[n], {n, 87}] (* _Ray Chandler_, Dec 20 2006 *)

%o (PARI) A126132(n) = sum(k=1,n,!(n%numdiv(k))); \\ _Antti Karttunen_, Apr 01 2021

%o (PARI) first(n) = { n = min(n, 245044799); qdivs = vector(960); res = vector(n); for(i = 1, n, nd = numdiv(i); qdivs[nd]++; d = select(x -> x <= #qdivs, divisors(i)); res[i] = sum(j = 1, #d, qdivs[d[j]]) ); res } \\ _David A. Corneth_, Apr 01 2021

%Y Cf. A000005, A002182, A126131.

%K nonn,look

%O 1,2

%A _Leroy Quet_, Dec 18 2006

%E Extended by _Ray Chandler_, Dec 20 2006