A322376 - OEIS

%I #10 Feb 16 2019 07:26:46

%S 1,3,4,6,7,8,13,14,15,20,30,31,38,40,44,57,62,63,68,74,102,110,121,

%T 127,133,138,150,158,164,174,183,194,198,200,212,230,242,255,258,278,

%U 282,284,307,314,318,332,338,348,350,354,368,374,380,398,402,410,422,458

%N Positive integers k that are the sum of divisors of some positive integer but there exists no divisor d where 1 < d, k/d of k such that d and k/d have this property.

%C Also number k such that k is in A002191 but there is no divisor d where 1 < d, k/d of k such that both d and k/d are in A002191. A002191 is closed under multiplication with terms in this sequence as primitive terms.

%e 4 is in A002191 as sigma(3) = 4 but no divisor of 4 as described above exists. The only candidate is 2 but 2 isn't in A002191.

%o (PARI) upto(n) = my(u = List(), t, res=List()); for(i=1, n, c=sigma(i); if(c<=n, listput(u, c))); listsort(u, 1); u=Vec(u); for(i=1, #u, t=1; d=divisors(u[i]); for(j=2, (#d + 1)\2, if(vecsearch(u, d[j]) > 0 && vecsearch(u, u[i]/d[j]) > 0, t=0; next(1))); if(t==1, listput(res, u[i]))); res

%Y Cf. A000203, A002191.

%K nonn

%O 1,2

%A _David A. Corneth_, Jan 24 2019