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

Author

David A. Corneth, Jan 24 2019

Keywords

• nonn

Comments

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.

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.
		

Crossrefs

Cf. A000203, A002191.

Programs

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