This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A384247 #6 May 27 2025 01:17:06
%S A384247 1,1,2,3,4,2,6,4,8,4,10,6,12,6,8,15,16,8,18,12,12,10,22,8,24,12,18,18,
%T A384247 28,8,30,16,20,16,24,24,36,18,24,16,40,12,42,30,32,22,46,30,48,24,32,
%U A384247 36,52,18,40,24,36,28,58,24,60,30,48,48,48,20,66,48,44,24
%N A384247 The number of integers from 1 to n whose largest divisor that is an infinitary divisor of n is 1.
%C A384247 Analogous to A047994, as A064380 is analogous to A116550.
%H A384247 Amiram Eldar, <a href="/A384247/b384247.txt">Table of n, a(n) for n = 1..10000</a>
%F A384247 Multiplicative with a(p^e) = p^e * (1 - 1/p^A006519(e)).
%F A384247 a(n) >= A091732(n), with equality if and only if n is in A138302.
%F A384247 a(n) <= A047994(n), with equality if and only if n is in A138302.
%F A384247 a(n) >= A000010(n), with equality if and only if n is an exponentially odd number (A268335).
%F A384247 a(n) is odd if and only if n = 1 or 2^(2^k) for k >= 0 (A001146). a(2^(2^k)) = 2^(2^k)-1.
%F A384247 Sum_{k=1..n} a(k) ~ c * n^2 / 2, where c = Product_{p prime} f(1/p) = 0.66718130416373472394..., and f(x) = 1 - (1-x)*Sum_{k>=1} x^(2^k)/(1-x^(2^k)).
%t A384247 f[p_, e_] := p^e*(1 - 1/p^(2^(IntegerExponent[e, 2]))); a[1] = 1; a[n_] := Times @@ f @@@ FactorInteger[n]; Array[a, 100]
%o A384247 (PARI) a(n) = {my(f = factor(n)); n * prod(i = 1, #f~, (1 - 1/f[i,1]^(1 << valuation(f[i,2], 2))));}
%Y A384247 Row lengths of A384246.
%Y A384247 Cf. A000010, A001146, A006519, A047994, A064380, A091732, A116550, A138302, A268335, A384248.
%K A384247 nonn,easy,mult
%O A384247 1,3
%A A384247 _Amiram Eldar_, May 23 2025