A322376 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.
1, 3, 4, 6, 7, 8, 13, 14, 15, 20, 30, 31, 38, 40, 44, 57, 62, 63, 68, 74, 102, 110, 121, 127, 133, 138, 150, 158, 164, 174, 183, 194, 198, 200, 212, 230, 242, 255, 258, 278, 282, 284, 307, 314, 318, 332, 338, 348, 350, 354, 368, 374, 380, 398, 402, 410, 422, 458
Offset: 1
Keywords
Examples
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.
Programs
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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
Comments