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.

3, 5, 7, 11, 13, 15, 17, 19, 21, 23, 27, 29, 31, 33, 35, 37, 39, 41, 43, 47, 51, 53, 55, 57, 59, 61, 63, 65, 67, 69, 71, 73, 77, 79, 83, 85, 87, 89, 91, 93, 95, 97, 99, 101, 103, 105, 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

Offset

1,1

Comments

Sequence obtained when A003961 is applied to A348738 and the terms are sorted into ascending order.

The first squares in this sequence are: 169, 361, 961, 1369, 1849, 2209, 2809, 3721, 4489, 5329, 6241, 6889, ...

Links

Table of n, a(n) for n=1..73.

Index entries for sequences computed from indices in prime factorization

Index entries for sequences related to sigma(n)

Mathematica

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 *)

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)};
isA348748(n) = ((n%2)&&(A064989(sigma(n)) < A064989(n)));

Crossrefs

Cf. A000203, A003961, A064989, A326042, A348738, A348749, A348938 (terms of A228058 that occur here).

Cf. also A348741, A348753.

Sequence in context: A175679 A088828 A348741 * A182318 A376218 A247424

Adjacent sequences: A348745 A348746 A348747 * A348749 A348750 A348751

Keyword

nonn

Author

Antti Karttunen, Nov 02 2021

Status

approved