A392347 - OEIS

%I #22 Feb 27 2026 08:37:31

%S 2,4,8,14,15,20,21,26,32,33,34,38,44,45,52,56,57,62,69,74,75,85,86,93,

%T 94,98,99,104,106,116,118,122,128,129,133,134,135,136,140,141,142,145,

%U 147,148,152,158,164,166,171,175,176,177,178,189,196,201,202,205,207,213,214,217,218,224,226,230

%N Numbers k such that A000005(k) = A000005(k/d + d) for some d.

%H Robert Israel, <a href="/A392347/b392347.txt">Table of n, a(n) for n = 1..10000</a>

%e 1 is not a term because A000005(1) = 1 < 2 = A000005(1/1 + 1).

%e 2 is a term because A000005(2) = A000005(2/1 + 1) = 2 for d = 1 or d = 2;

%e 4 is a term because A000005(4) = A000005(4/2 + 2) = 3 for only d = 2.

%p filter:= proc(n) local t; uses NumberTheory;

%p   t:= tau(n);

%p   ormap(d -> tau(n/d+d) = t, Divisors(n))

%p end proc:

%p select(filter, [$1..300]); # _Robert Israel_, Jan 08 2026

%t Select[Range[230],Sum[Boole[DivisorSigma[0,#]==DivisorSigma[0,#/d+d]],{d,Divisors[#]}]>0 &] (* _Stefano Spezia_, Jan 08 2026 *)

%o (Magma) [k: k in [1..230] | not #[d: d in Divisors(k) | #Divisors(k) eq #Divisors((k div d) + d)] eq 0];

%o (PARI) isok(k) = #select(x->(x==numdiv(k)), apply(x->numdiv(k/x+x), divisors(k))); \\ _Michel Marcus_, Jan 08 2026

%Y Cf. A000005, A161904, A391496.

%Y Superset of A005237.

%K nonn

%O 1,1

%A _Juri-Stepan Gerasimov_, Jan 07 2026