A348749 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.

9, 25, 45, 49, 75, 81, 117, 121, 225, 243, 289, 325, 333, 405, 441, 529, 549, 605, 625, 657, 675, 729, 841, 925, 1053, 1089, 1125, 1215, 1225, 1413, 1445, 1521, 1525, 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

Offset: 1

Author

Antti Karttunen, Nov 02 2021

Keywords

• nonn

Comments

Sequence obtained when A003961 is applied to A348739 and the terms are sorted into ascending order.

From Robert Israel, Nov 12 2024: (Start)

If a and b are terms and are coprime, then a * b is a term.

If p > 2 is in A053182, Legendre's conjecture implies p^2 is in this sequence. (End)

Links

• Robert Israel, Table of n, a(n) for n = 1..10000
• Index entries for sequences computed from indices in prime factorization
• Index entries for sequences related to sigma(n)

Crossrefs

Cf. A000203, A003961, A053182, A064989, A326042, A348739, A348748, A348939 (terms of A228058 that occur here).

Cf. also A348742, A348754.

Programs

Maple

g:= prevprime: g(2):= 1:
f:= proc(n) local F,t;
  F:= ifactors(n)[2];
  mul(g(t[1])^t[2],t=F)
end proc:
select(t -> f(numtheory:-sigma(t)) > f(t), [seq(i,i=1..4000,2)]); # Robert Israel, Nov 12 2024

Mathematica

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 *)

PARI

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)};
isA348749(n) = ((n%2)&&(A064989(sigma(n)) > A064989(n)));