%I #18 Nov 13 2024 17:00:02
%S 9,25,45,49,75,81,117,121,225,243,289,325,333,405,441,529,549,605,625,
%T 657,675,729,841,925,1053,1089,1125,1215,1225,1413,1445,1521,1525,
%U 1575,1665,1681,1737,1825,1875,2025,2205,2401,2475,2493,2601,2817,2825,2925,2997,3025,3033,3125,3249,3481,3573,3645,3675,3789
%N Odd numbers k for which A064989(sigma(k)) > A064989(k), where A064989 shifts the prime factorization one step towards lower primes, and sigma is the sum of divisors function.
%C Sequence obtained when A003961 is applied to A348739 and the terms are sorted into ascending order.
%C From _Robert Israel_, Nov 12 2024: (Start)
%C If a and b are terms and are coprime, then a * b is a term.
%C If p > 2 is in A053182, Legendre's conjecture implies p^2 is in this sequence. (End)
%H Robert Israel, <a href="/A348749/b348749.txt">Table of n, a(n) for n = 1..10000</a>
%H <a href="/index/Pri#prime_indices">Index entries for sequences computed from indices in prime factorization</a>
%H <a href="/index/Si#SIGMAN">Index entries for sequences related to sigma(n)</a>
%p g:= prevprime: g(2):= 1:
%p f:= proc(n) local F,t;
%p F:= ifactors(n)[2];
%p mul(g(t[1])^t[2],t=F)
%p end proc:
%p select(t -> f(numtheory:-sigma(t)) > f(t), [seq(i,i=1..4000,2)]); # _Robert Israel_, Nov 12 2024
%t f[2, e_] := 1; f[p_, e_] := NextPrime[p, -1]^e; s[1] = 1; s[n_] := Times @@ f @@@ FactorInteger[n]; Select[Range[1, 4000, 2], s[DivisorSigma[1, #]] > s[#] &] (* _Amiram Eldar_, Nov 04 2021 *)
%o (PARI)
%o A064989(n) = {my(f); f = factor(n); if((n>1 && f[1,1]==2), f[1,2] = 0); for (i=1, #f~, f[i,1] = precprime(f[i,1]-1)); factorback(f)};
%o isA348749(n) = ((n%2)&&(A064989(sigma(n)) > A064989(n)));
%Y Cf. A000203, A003961, A053182, A064989, A326042, A348739, A348748, A348939 (terms of A228058 that occur here).
%Y Cf. also A348742, A348754.
%K nonn
%O 1,1
%A _Antti Karttunen_, Nov 02 2021