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

1,1

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)

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 *)

Prog

(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)));

Crossrefs

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

Cf. also A348742, A348754.

Sequence in context: A227518 A031036 A371086 * A291259 A051132 A247687

Adjacent sequences: A348746 A348747 A348748 * A348750 A348751 A348752

Keyword

nonn

Author

Antti Karttunen, Nov 02 2021

Status

approved