

A175388


Numbers n such that the sum of the divisors of n is semiprime.


1



3, 5, 8, 13, 18, 36, 37, 49, 50, 61, 73, 81, 100, 121, 144, 157, 169, 193, 225, 256, 277, 313, 361, 397, 400, 421, 457, 529, 541, 576, 578, 613, 625, 661, 673, 733, 757, 841, 877, 961, 997, 1024, 1093, 1153, 1156, 1201, 1213, 1237, 1321, 1381, 1453
(list;
graph;
refs;
listen;
history;
text;
internal format)



OFFSET

1,1


COMMENTS

The sequence contains a subset of squares {36, 49, 81, 100, 121, 144, 169, 225, 256, ...}.
If n is a term of this sequence and n is nonsquare, then n must be a prime or twice a square. Additionally, if n is in this sequence, then A001221(n) <= 2.  Altug Alkan, Jul 17 2016


LINKS

G. C. Greubel, Table of n, a(n) for n = 1..1000


EXAMPLE

a(6)= 36 with 8 divisors: {1, 2, 3, 4, 6, 9, 12, 18, 36}
and the sum of the divisors is 91 = 7*13 (semiprime).


MAPLE

with(numtheory):for k from 1 to 1600 do:if bigomega(sigma(k))=2 then printf(`%d, `, k): else fi:od:


MATHEMATICA

Select[Range@ 1500, PrimeOmega@ DivisorSigma[1, #] == 2 &] (* Michael De Vlieger, Jul 17 2016 *)


CROSSREFS

Cf. A112381, A023194 (numbers n such that sigma(n) is prime).
Sequence in context: A265046 A158384 A053651 * A310037 A104563 A261175
Adjacent sequences: A175385 A175386 A175387 * A175389 A175390 A175391


KEYWORD

nonn


AUTHOR

Michel Lagneau, Aug 20 2011


STATUS

approved



