A348739 Numbers k for which A326042(k) > k.

4, 9, 12, 16, 18, 25, 32, 36, 44, 48, 49, 64, 72, 81, 96, 99, 100, 108, 124, 144, 147, 162, 169, 176, 180, 192, 196, 225, 236, 243, 252, 256, 279, 284, 288, 300, 320, 324, 361, 372, 396, 400, 405, 432, 441, 448, 450, 468, 484, 486, 496, 507, 512, 529, 531, 567, 576, 588, 604, 612, 625, 639, 648, 675, 676, 700, 704

Offset: 1

Author

Antti Karttunen, Nov 02 2021

Keywords

• nonn

Comments

Terms that occur also in A337386 are: 180, 300, 720, 900, 960, 1008, 1200, 1440, 1620, 1800, 2016, 2400, ...

Links

• Index entries for sequences computed from indices in prime factorization
• Index entries for sequences related to sigma(n)

Crossrefs

Positions of negative terms in A348736.

Cf. A326182 (subsequence after its initial 1), A348738.

Cf. A000203, A003961, A064989, A161942, A191218, A326042, A337386, A348742, A348749 (corresponding odd numbers), A348942.

Programs

Mathematica

f1[2, e_] := 1; f1[p_, e_] := NextPrime[p, -1]^e; s1[1] = 1; s1[n_] := Times @@ f1 @@@ FactorInteger[n]; f2[p_, e_] := NextPrime[p]^e; s2[1] = 1; s2[n_] := Times @@ f2 @@@ FactorInteger[n]; Select[Range[700], s1[DivisorSigma[1, s2[#]]] > # &] (* Amiram Eldar, Nov 04 2021 *)

PARI

A003961(n) = my(f = factor(n)); for (i=1, #f~, f[i, 1] = nextprime(f[i, 1]+1)); factorback(f); \\ From A003961
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)};
A326042(n) = A064989(sigma(A003961(n)));
isA348739(n) = (A326042(n)>n);