A334112 a(n) = A332809(n) - A000005(n).

0, 0, 1, 0, 2, 1, 4, 0, 3, 2, 5, 1, 6, 5, 6, 0, 4, 3, 8, 2, 8, 6, 9, 1, 6, 7, 6, 6, 11, 6, 13, 0, 13, 4, 14, 3, 11, 10, 11, 2, 9, 9, 16, 7, 12, 11, 14, 1, 15, 6, 10, 8, 13, 6, 12, 7, 13, 13, 16, 6, 17, 16, 14, 0, 18, 15, 22, 4, 22, 16, 23, 3, 14, 13, 15, 12, 26, 12, 19, 2, 10, 10, 13, 10, 12, 20, 21, 8, 15, 12, 24, 13, 23

Offset: 1

Author

Antti Karttunen, May 09 2020

Keywords

• nonn

Links

• Antti Karttunen, Table of n, a(n) for n = 1..16384
• Antti Karttunen, Data supplement: n, a(n) computed for n = 1..65537

Crossrefs

Cf. A000005, A000079 (positions of zeros), A007283, A332809.

Programs

Mathematica

Array[Block[{w = {{#}}}, While[w[[-1]] != {1}, w = Join[w, {Union@ Flatten[# - #/FactorInteger[#][[All, 1]] & /@ w[[-1]] ]}]]; Length@ Union@ Flatten@ w - DivisorSigma[0, #]] &, 93] (* Michael De Vlieger, May 09 2020, after Robert G. Wilson v at A332809 *)

PARI

up_to = 20000;
A332809list(up_to) = { my(v=vector(up_to)); v[1] = Set([1]); for(n=2,up_to, my(f=factor(n)[, 1]~, s=Set([n])); for(i=1,#f,s = setunion(s,v[n-(n/f[i])])); v[n] = s); apply(length,v); }
v332809 = A332809list(up_to);
A332809(n) = v332809[n];
A334112(n) = (A332809(n) - numdiv(n));

Formula

a(n) = A332809(n) - A000005(n).

a(2^n) = 0 for all n >= 0.