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A267696 Numbers with 5 odd divisors.

%I A267696 #43 Sep 16 2024 02:10:17
%S A267696 81,162,324,625,648,1250,1296,2401,2500,2592,4802,5000,5184,9604,
%T A267696 10000,10368,14641,19208,20000,20736,28561,29282,38416,40000,41472,
%U A267696 57122,58564,76832,80000,82944,83521,114244,117128,130321,153664,160000,165888,167042,228488,234256,260642,279841
%N A267696 Numbers with 5 odd divisors.
%C A267696 Positive integers that have exactly five odd divisors.
%C A267696 Numbers k such that the symmetric representation of sigma(k) has 5 subparts. - _Omar E. Pol_, Dec 28 2016
%C A267696 Also numbers that can be expressed as the sum of k > 1 consecutive positive integers in exactly 4 ways; e.g., 81 = 40+41 = 26+27+28 = 11+12+13+14+15+16 = 5+6+7+8+9+10+11+12+13. - _Julie Jones_, Aug 13 2018
%H A267696 Amiram Eldar, <a href="/A267696/b267696.txt">Table of n, a(n) for n = 1..10000</a>
%F A267696 A001227(a(n)) = 5.
%F A267696 Sum_{n>=1} 1/a(n) = 2 * P(4) - 1/8 = 0.00289017370127..., where P(4) is the value of the prime zeta function at 4 (A085964). - _Amiram Eldar_, Sep 16 2024
%o A267696 (PARI) isok(n) = sumdiv(n, d, (d%2)) == 5; \\ _Michel Marcus_, Apr 03 2016
%o A267696 (GAP) A:=List([1..700000],n->DivisorsInt(n));;
%o A267696 B:=List([1..Length(A)],i->Filtered(A[i],IsOddInt));;
%o A267696 a:=Filtered([1..Length(B)],i->Length(B[i])=5); # _Muniru A Asiru_, Aug 14 2018
%Y A267696 Column 5 of A266531.
%Y A267696 Cf. A001227, A030514, A038547, A085964, A236104, A237593, A279387.
%Y A267696 Numbers with k odd divisors (k = 1..10): A000079, A038550, A072502, apparently A131651, this sequence, A230577, A267697, A267891, A267892, A267893.
%K A267696 nonn
%O A267696 1,1
%A A267696 _Omar E. Pol_, Apr 03 2016
%E A267696 More terms from _Michel Marcus_, Apr 03 2016