A326134 Numbers k such that A326057(k) is equal to A252748(k) and A252748(k) is not 1.

6, 28, 69, 91, 496, 2211, 4825, 8128, 12639, 22799825, 33550336, 60406599, 68258725, 569173299, 794579511, 984210266, 2830283326, 8589869056, 10759889913, 80295059913, 85871289682

Offset

1,1

Comments

No other terms below 3221225472.

Numbers k such that A252748(k) [= A003961(k) - 2*k] <> 1 (i.e., k is not in A348514), and A286385(k) [= A003961(k) - A000203(k)] = m*A252748(k) for some positive integer m. Note that this entails that k is nonabundant (A000203(k) <= 2*k) and primeshift-abundant (A252748(k) > 2), thus this is a subsequence of A341614. - revised Dec 13 2024

This is a subsequence of A378980, see further comments there. - Antti Karttunen, Dec 13 2024

Links

Table of n, a(n) for n=1..21.

Index entries for sequences where any odd perfect numbers must occur

Index entries for sequences computed from indices in prime factorization

Index entries for sequences related to sigma(n)

Example

28 is a term as A252748(28) = 43 > 1 and A286385(28) = 43, which is a multiple of 43.
69 is a term as A252748(69) = 7 > 1 and A286385(69) = 49 is a multiple of 7.
91 is a term as A252748(91) = 5 > 1 and A286385(91) = 75 is a multiple of 5.

Mathematica

Select[Range[10^5], And[#3 - #1 != 1, GCD[#3 - #1, #3 - #2] == #3 - #1] & @@ {2 #, DivisorSigma[1, #], Times @@ Map[#1^#2 & @@ # &, FactorInteger[#] /. {p_, e_} /; e > 0 :> {Prime[PrimePi@ p + 1], e}] - Boole[# == 1]} &] (* Michael De Vlieger, Feb 22 2021 *)

Prog

(PARI)
A003961(n) = my(f = factor(n)); for (i=1, #f~, f[i, 1] = nextprime(f[i, 1]+1)); factorback(f); \\ From A003961
isA326134(n) = { my(s = A003961(n), t = (s-(2*n)), u = s-sigma(n)); ((1!=t)&&!(u%t)&&((u/t)>0)); };

Crossrefs

Cf. A000396 (subsequence), A003961, A252748, A286385, A326057, A337345, A337372, A341611, A348514, A379216, A379217.

Subsequence of the following sequences: A246282, A341614, A378980.

Odd terms form a subsequence of A349753.

Sequence in context: A034955 A117978 A119174 * A343512 A326484 A144945

Adjacent sequences: A326131 A326132 A326133 * A326135 A326136 A326137

Keyword

nonn,more

Author

Antti Karttunen, Jun 11 2019

Extensions

a(18) from Antti Karttunen, Dec 14 2024

a(19)..a(21) from Antti Karttunen (from the b-file of A378980 computed by Amiram Eldar), Dec 20 2024

Status

approved