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

1,1

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

Table of n, a(n) for n=1..16.

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

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 *)

Prog

(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))));

Crossrefs

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

Subsequence of A343218.

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

Sequence in context: A158414 A031740 A031529 * A031709 A158413 A252413

Adjacent sequences: A347881 A347882 A347883 * A347885 A347886 A347887

Keyword

nonn,more

Author

Antti Karttunen, Sep 19 2021

Status

approved