A329104 Numbers m such that sigma(m) - tau(m) = 2m.

56, 7192, 7232, 7912, 10792, 17272, 30592, 114256, 2154584, 3428368, 89245784, 36993585958528, 118122891971648, 943226995376128, 2737657760695168, 5020331545072768, 36028789368553472, 40256362055287184, 42381542060395136, 950808877965961856, 2616769087480013696, 3515864044679266304, 4611826686121443328, 9223371897268338688

Offset

1,1

Comments

Abundant numbers m with abundance A(m) = tau(m).

Corresponding values of A(m) = tau(m): 8, 16, 14, 16, 16, 16, 16, 20, 32, 30, 32, ...

Links

Max Alekseyev, Table of n, a(n) for n = 1..45

Example

Number 56 is in the sequence because sigma(56) - tau(56) = 2*56; 120 - 8 = 112.

Mathematica

Select[Range[4*10^6], DivisorSigma[1, #] - DivisorSigma[0, #] == 2 # &] (* Amiram Eldar, Nov 04 2019 *)

Prog

(Magma) [m: m in [1..10^5] | SumOfDivisors(m) - NumberOfDivisors(m) eq 2*m];
(PARI) isok(m) = my(f=factor(m)); sigma(f) - numdiv(f) == 2*m; \\ Michel Marcus, Nov 05 2019

Crossrefs

Subsequence of A056075.

Cf. A000005, A000203, A033880, A065608, A083874.

Sequence in context: A180372 A255960 A201240 * A233428 A183614 A082167

Adjacent sequences: A329101 A329102 A329103 * A329105 A329106 A329107

Keyword

nonn,changed

Author

Jaroslav Krizek, Nov 04 2019

Extensions

a(11) from Amiram Eldar, Nov 04 2019

a(12)-a(14) from Jud McCranie, Jan 21 2026

a(15)-a(24) from Max Alekseyev, Jun 24 2026

Status

approved