A393494 Starts of runs of 3 consecutive integers that are all s-practical numbers (A393492).

1, 59, 71, 107, 179, 191, 239, 269, 311, 419, 431, 599, 659, 809, 827, 1019, 1091, 1151, 1319, 1427, 1487, 1619, 1871, 1931, 2087, 2111, 2267, 2309, 2339, 2591, 2687, 2729, 2969, 2999, 3119, 3167, 3299, 3359, 3527, 3539, 3671, 4019, 4049, 4127, 4157, 4158, 4259, 4271

Offset

1,2

Links

Amiram Eldar, Table of n, a(n) for n = 1..10000

Mathematica

sPracQ[n_] := sPracQ[n] = Module[{sd = Sort[Map[DivisorSigma[1, #] - # &, Divisors[n]]], sm, ac}, sm = Plus @@ sd; ac = Accumulate[sd]; AllTrue[Range[Length[sd] - 1], sd[[# + 1]] <= 1 + ac[[#]] &]];
Select[Partition[Range[4300], 3, 1], AllTrue[#, sPracQ] &][[;; , 1]]

Prog

(PARI) issprac(k) = {my(sd = vecsort(apply(x -> sigma(x) - x, divisors(k))), sm = vecsum(sd), s = 0); for(i = 1, #sd-1, s += sd[i]; if(sd[i+1] > 1 + s, return(0))); 1; }
isok(k) = issprac(k) && issprac(k+1) && issprac(k+2);

Crossrefs

Subsequence of A393492 and A393493.

A393495 is a subsequence.

Sequence in context: A316971 A162000 A080192 * A126693 A139938 A033235

Adjacent sequences: A393491 A393492 A393493 * A393495 A393496 A393497

Keyword

nonn

Author

Amiram Eldar, Feb 16 2026

Status

approved