cp's OEIS Frontend

A348748 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.

%I A348748 #11 Nov 04 2021 20:46:28
%S A348748 3,5,7,11,13,15,17,19,21,23,27,29,31,33,35,37,39,41,43,47,51,53,55,57,
%T A348748 59,61,63,65,67,69,71,73,77,79,83,85,87,89,91,93,95,97,99,101,103,105,
%U A348748 107,109,111,113,115,119,123,125,127,129,131,133,135,137,139,141,143,145,147,149,151,153,155,157,159,161,163
%N A348748 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 A348748 Sequence obtained when A003961 is applied to A348738 and the terms are sorted into ascending order.
%C A348748 The first squares in this sequence are: 169, 361, 961, 1369, 1849, 2209, 2809, 3721, 4489, 5329, 6241, 6889, ...
%H A348748 <a href="/index/Pri#prime_indices">Index entries for sequences computed from indices in prime factorization</a>
%H A348748 <a href="/index/Si#SIGMAN">Index entries for sequences related to sigma(n)</a>
%t A348748 f[2, e_] := 1; f[p_, e_] := NextPrime[p, -1]^e; s[1] = 1; s[n_] := Times @@ f @@@ FactorInteger[n]; Select[Range[1, 200, 2], s[DivisorSigma[1, #]] < s[#] &] (* _Amiram Eldar_, Nov 04 2021 *)
%o A348748 (PARI)
%o A348748 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 A348748 isA348748(n) = ((n%2)&&(A064989(sigma(n)) < A064989(n)));
%Y A348748 Cf. A000203, A003961, A064989, A326042, A348738, A348749, A348938 (terms of A228058 that occur here).
%Y A348748 Cf. also A348741, A348753.
%K A348748 nonn
%O A348748 1,1
%A A348748 _Antti Karttunen_, Nov 02 2021