

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.


0



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
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OFFSET

1,2


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.


LINKS

Table of n, a(n) for n=1..58.


EXAMPLE

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.


PROG

(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


CROSSREFS

Cf. A000203, A002191.
Sequence in context: A085149 A239458 A007370 * A044813 A154661 A275672
Adjacent sequences: A322373 A322374 A322375 * A322377 A322378 A322379


KEYWORD

nonn


AUTHOR

David A. Corneth, Jan 24 2019


STATUS

approved



