%I #35 Sep 16 2024 02:10:21

%S 729,1458,2916,5832,11664,15625,23328,31250,46656,62500,93312,117649,

%T 125000,186624,235298,250000,373248,470596,500000,746496,941192,

%U 1000000,1492992,1771561,1882384,2000000,2985984,3543122,3764768,4000000,4826809,5971968,7086244,7529536,8000000,9653618

%N Numbers with 7 odd divisors.

%C Positive integers that have exactly seven odd divisors.

%C Numbers k such that the symmetric representation of sigma(k) has 7 subparts. - _Omar E. Pol_, Dec 28 2016

%C Numbers that can be formed in exactly 6 ways by summing sequences of 2 or more consecutive positive integers. - _Julie Jones_, Aug 13 2018

%C Numbers of the form p^6 * 2^k where p is an odd prime. - _David A. Corneth_, Aug 14 2018

%H David A. Corneth, <a href="/A267697/b267697.txt">Table of n, a(n) for n = 1..10000</a>

%F A001227(a(n)) = 7.

%F Sum_{n>=1} 1/a(n) = 2 * P(6) - 1/32 = 0.00289017370127..., where P(6) is the value of the prime zeta function at 6 (A085966). - _Amiram Eldar_, Sep 16 2024

%o (PARI) isok(n) = sumdiv(n, d, (d%2)) == 7; \\ _Michel Marcus_, Apr 03 2016

%o (PARI) upto(n) = {my(res = List()); forprime(p = 3, sqrtnint(n, 6), listput(res, p^6)); q = #res; for(i = 1, q, odd = res[i]; for(j = 1, logint(n \ odd, 2), listput(res, odd <<= 1))); listsort(res); res} \\ _David A. Corneth_, Aug 14 2018

%Y Column 7 of A266531.

%Y Cf. A001227, A030516, A038547, A085966, A236104, A237593, A279387.

%Y Numbers with k odd divisors (k = 1..10): A000079, A038550, A072502, apparently A131651, A267696, A230577, this sequence, A267891, A267892, A267893.

%K nonn,easy

%O 1,1

%A _Omar E. Pol_, Apr 03 2016

%E More terms from _Michel Marcus_, Apr 03 2016