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URL: https://oeis.org/A393157

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A393157
Smallest positive number m such that A000538(m) is divisible by n.
1
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
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
KEYWORD
nonn,easy
AUTHOR
Paolo P. Lava, Feb 03 2026
STATUS
approved