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A389463
Numbers k for which A389461(k) is a positive multiple of (k-A075423(k)).
2
6, 28, 30, 42, 66, 70, 78, 102, 114, 138, 174, 186, 210, 222, 246, 258, 282, 318, 330, 354, 366, 390, 402, 426, 438, 462, 474, 496, 498, 510, 534, 546, 570, 582, 606, 618, 642, 654, 678, 690, 714, 762, 770, 786, 798, 822, 834, 858, 870, 894, 906, 910, 930, 942, 966, 978, 1002, 1038, 1074, 1086, 1110, 1122, 1146
OFFSET
1,1
COMMENTS
Numbers k for which A389460(k) > k (equally: A001065(k) >= A007947(n)) and A389461(k) is a multiple of (k-A075423(k)).
Question: Is this disjoint union of A000396 and A087248?
First odd terms: 15015, 19635, 21945, ...
FORMULA
{k | A389461(k) > 0, A389461(k) == 0 mod (k-A075423(k))}.
MATHEMATICA
A389463Q[k_] := With[{m = DivisorSigma[1, k] - # - k}, m > 0 && Divisible[m, k - #]] & [Times @@ FactorInteger[k][[All, 1]] - 1];
Select[Range[1500], A389463Q] (* Paolo Xausa, Oct 07 2025 *)
PROG
(PARI)
A389461(n) = (1+(sigma(n)-factorback(factor(n)[, 1]))-n);
is_A389463(k) = { my(x=A389461(k), y=(factorback(factor(k)[, 1])-1)); (x>0 && !(x%(k-y))); };
CROSSREFS
Subsequence of A389462.
Subsequences: A000396, A087248.
Sequence in context: A261868 A379499 A342922 * A357462 A105402 A362805
KEYWORD
nonn
AUTHOR
Antti Karttunen, Oct 07 2025
STATUS
approved