A393495 Starts of runs of 4 consecutive integers that are all s-practical numbers (A393492).

4157, 10528, 11968, 23560, 33149, 43648, 148301, 153269, 161728, 246509, 281248, 312928, 359477, 388960, 396197, 455488, 455597, 457000, 464128, 503549, 518237, 632500, 640528, 706048, 815669, 882880, 887920, 906749, 1096829, 1168397, 1235248, 1265920, 1334717

Offset

1,1

Comments

The least start of a run of 5 consecutive integers that are all s-practical numbers is a(8466) = 744540496.

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[10^5], 4, 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) && issprac(k+3);

Crossrefs

Subsequence of A393492, A393493 and A393494.

Sequence in context: A145205 A243025 A196494 * A104824 A168663 A043627

Adjacent sequences: A393492 A393493 A393494 * A393496 A393497 A393498

Keyword

nonn

Author

Amiram Eldar, Feb 16 2026

Status

approved