cp's OEIS Frontend

A348754 Numbers k congruent to 1 or 5 mod 6, for which A064989(A064989(sigma(k))) > A064989(A064989(k)), where A064989 shifts the prime factorization one step towards lower primes, and sigma is the sum of divisors function.

%I A348754 #14 Nov 04 2021 20:46:50
%S A348754 25,49,121,169,175,275,289,325,625,841,925,1225,1445,1525,1675,1681,
%T A348754 1825,2401,3025,3125,3481,3757,3925,4075,4225,4375,4825,5041,5275,
%U A348754 5929,6125,6875,6925,7075,7225,7825,7921,8125,8275,8281,9025,9925,10201,10525,10625,10693,11425,11875,12005,12025,13075,13225,13475
%N A348754 Numbers k congruent to 1 or 5 mod 6, for which A064989(A064989(sigma(k))) > A064989(A064989(k)), where A064989 shifts the prime factorization one step towards lower primes, and sigma is the sum of divisors function.
%C A348754 Sequence A003961(A003961(A348752(n))), n=1.., sorted into ascending order.
%C A348754 Not a subsequence of A348749. The first terms that occur here but not there are: 169, 175, 275, 1675, 3757, 4075, 5275, 7075, 8275, 10693, 12025, ...
%H A348754 <a href="/index/Pri#prime_indices">Index entries for sequences computed from indices in prime factorization</a>
%H A348754 <a href="/index/Si#SIGMAN">Index entries for sequences related to sigma(n)</a>
%t A348754 f[2, e_] := 1; f[p_, e_] := NextPrime[p, -1]^e; s[1] = 1; s[n_] := Times @@ f @@@ FactorInteger[n]; Select[Range[15000], MemberQ[{1, 5}, Mod[#, 6]] && s[s[DivisorSigma[1, #]]] > s[s[#]] &] (* _Amiram Eldar_, Nov 04 2021 *)
%o A348754 (PARI)
%o A348754 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 A348754 isA348754(n) = ((n%2)&&(n%3)&&(A064989(A064989(sigma(n))) > A064989(A064989(n))));
%Y A348754 Cf. A003961, A007310, A064989, A348750, A348752, A348753.
%Y A348754 Cf. also A348749, A348932, A348936 (square roots of squares present).
%K A348754 nonn
%O A348754 1,1
%A A348754 _Antti Karttunen_, Nov 04 2021