A393157 Smallest positive number m such that A000538(m) is divisible by n.

1, 3, 4, 7, 6, 4, 3, 15, 13, 12, 5, 8, 6, 3, 18, 31, 2, 27, 9, 24, 13, 11, 11, 31, 6, 12, 40, 7, 14, 31, 15, 63, 22, 8, 6, 40, 14, 19, 13, 31, 18, 27, 8, 16, 81, 11, 10, 31, 3, 124, 8, 32, 26, 40, 43, 31, 9, 28, 4, 31, 30, 15, 13, 127, 6, 27, 19, 8, 22, 24, 35

Offset

1,2

Links

Paolo P. Lava, Table of n, a(n) for n = 1..10000

Formula

a(2^j) = 2^(j+1) - 1.

a(p^j) = (p^(j+1) - 1)/2 for primes 3, 11, ...

a(p^j) = (p^j - 1)/2 for primes 7, 13, 19, 23, 29, ...

Maple

F:= proc(n) local x; min(map(t -> rhs(op(t)), subs({x=0}=NULL, [msolve(x*(x+1)*(2*x+1)*(3*x^2+3*x-1)/30, n)]))) end proc:
F(1):= 1:
map(F, [$1..120]); # Robert Israel, Feb 11 2026

Mathematica

Table[s = k = 1; While[! Divisible[s, n], k++; s += k^4]; k, {n, 120}] (* Michael De Vlieger, Feb 11 2026 *)

Prog

(PARI) a(n) = my(k=1); while (k*(1+k)*(1+2*k)*(-1+3*k+3*k^2)/30 % n, k++); k; \\ Michel Marcus, Feb 10 2026
(Python)
from itertools import count
def A393157(n): return next(m for m in count(1) if not m*(m**2*(m*(6*m+15)+10)-1)//30 % n) # Chai Wah Wu, Feb 17 2026

Crossrefs

Cf. A000538, A011772, A383075, A383972.

Sequence in context: A348987 A322656 A105827 * A396319 A230289 A367502

Adjacent sequences: A393154 A393155 A393156 * A393158 A393159 A393160

Keyword

nonn,easy

Author

Paolo P. Lava, Feb 03 2026

Status

approved