A364286 - OEIS

%I #23 Mar 10 2024 20:01:30

%S 33,51,69,91,99,135,141,145,153,159,187,207,213,217,285,295,303,321,

%T 339,391,411,423,427,435,445,477,507,519,573,637,639,679,681,699,771,

%U 783,799,843,855,861,885,895,901,909,933,951,963,1017,1041,1057,1059,1071,1081,1083,1147,1149,1173,1185,1195,1203,1207

%N Composite numbers k for which A324644(k)/A324198(k) = 2.

%C See comments in A351458.

%C All terms are odd. Of the 63 initial terms of A349169, only term 13923 occurs also in this sequence. The first common term with A332458 is 161257. - _Antti Karttunen_, Mar 10 2024

%H Antti Karttunen, <a href="/A364286/b364286.txt">Table of n, a(n) for n = 1..20000</a>

%H <a href="/index/O#opnseqs">Index entries for sequences where odd perfect numbers must occur, if they exist at all</a>

%H <a href="/index/Pri#primorialbase">Index entries for sequences related to primorial base</a>

%H <a href="/index/Si#SIGMAN">Index entries for sequences related to sigma(n)</a>

%t f[x_] := Block[{m, i, n = x, p}, m = i = 1; While[n > 0, p = Prime[i]; m *= p^Mod[n, p]; n = Quotient[n, p]; i++]; m]; Select[Select[Range[1350], CompositeQ], GCD[#2, #3]/GCD[#1, #3] == 2 & @@ {#, DivisorSigma[1, #], f[#]} &] (* _Michael De Vlieger_, Mar 10 2024 *)

%o (PARI)

%o A276086(n) = { my(m=1, p=2); while(n, m *= (p^(n%p)); n = n\p; p = nextprime(1+p)); (m); };

%o isA364286(n) = if(isprime(n), 0, my(u=A276086(n)); (gcd(sigma(n),u)==2*gcd(n,u))); \\ _Antti Karttunen_, Mar 10 2024

%Y Cf. A000203, A276086, A324198, A324644, A332458, A349169, A351458, A371082 (subsequence).

%Y Subsequence of A082686.

%K nonn

%O 1,1

%A _Antti Karttunen_, Jul 17 2023