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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.
9
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, ...
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
KEYWORD
nonn
AUTHOR
Antti Karttunen, Nov 02 2021
STATUS
approved