A347884 Odd composites k for which A003415(sigma(k))-k is strictly positive and a multiple of A003415(k). Here A003415 is the arithmetic derivative.

963, 969, 5871, 10479, 2308203, 41240261, 52024391, 69989429, 75384301, 319255721, 634457761, 781718149, 1184197307, 1190942957, 1195786661, 2114464203

Offset: 1

Author

Antti Karttunen, Sep 19 2021

Keywords

• nonn
• more

Comments

Odd nonprimes k for which A343223(k) = A003415(k).

Any odd terms of A065997, including odd perfect numbers, odd triperfect numbers and odd 5-multiperfect numbers, should occur in this sequence, if such numbers exist at all.

The odd terms present in A342924 form a subsequence of this sequence.

Links

• Index entries for sequences where odd perfect numbers must occur, if they exist at all

Crossrefs

Cf. A000203, A003415, A007691, A065997, A342925, A342926, A343223.

Subsequence of A343218.

Cf. also A000396, A005820, A046060, A342922, A342923, A342924, A347872, A347880.

Programs

Mathematica

ad[1] = 0; ad[n_] := n * Total@(Last[#]/First[#]& /@ FactorInteger[n]); Select[Range[1, 2.5*10^6, 2], CompositeQ[#] && (d = ad[DivisorSigma[1, #]] - #) > 0 && Divisible[d, ad[#]] &] (* Amiram Eldar, Sep 19 2021 *)

PARI

A003415(n) = if(n<=1, 0, my(f=factor(n)); n*sum(i=1, #f~, f[i, 2]/f[i, 1]));
isA347884(n) = if(!(n%2)||isprime(n),0,my(u=(A003415(sigma(n))-(n))); ((u>0)&&!(u%A003415(n))));