A387406 Numbers k such that sigma(A253560(k)) / A253560(k) is equal to (sigma(k)+1) / k, where A253560(k) = k multiplied by its largest prime factor.

6, 18, 28, 54, 117, 162, 196, 486, 496, 775, 1372, 1458, 1521, 4374, 8128, 9604, 13122, 15376, 19773, 24025, 39366, 67228, 88723, 118098, 257049, 354294, 470596, 476656, 744775, 796797, 1032256, 1062882, 2896363, 3188646, 3294172, 3341637, 6725201, 9565938, 12326221, 14776336, 23059204, 23088025, 25774633, 27237961

Offset

1,1

Comments

Terms k for which sigma(k/A053585(k)) = A006530(k). This further entails that A001221(k) = 2 [See A023194].

Links

Antti Karttunen, Table of n, a(n) for n = 1..58 (larger b-file needed)

C. A. Holdener and J. A. Holdener, Characterizing Quasi-Friendly Divisors, Journal of Integer Sequences, Vol. 23 (2020), Article 20.8.4.

Index entries for sequences related to sigma(n)

Mathematica

fk[k_]:=k*FactorInteger[k][[-1, 1]]; Select[Range[10^6], DivisorSigma[1, fk[#]]/fk[#]==(DivisorSigma[1, #]+1)/#&] (* James C. McMahon, Aug 31 2025 *)

Prog

(PARI)
A253560(n) = if (n==1, 1, n*vecmax(factor(n)[, 1]));
isA387406(n) = { my(x=A253560(n)); ((sigma(x)/x) == ((sigma(n)+1)/n)); };

Crossrefs

Cf. A000203, A001221, A006530, A023194, A053585, A253560, A387405.

Subsequences: A000396 (even terms only), A240991 (conjectured, if true, then A000396 has only even terms).

Sequence in context: A355228 A352061 A225110 * A077660 A240991 A304050

Adjacent sequences: A387403 A387404 A387405 * A387407 A387408 A387409

Keyword

nonn

Author

Antti Karttunen, Aug 30 2025

Status

approved