A381133 If n = (p_1^e_1)*(p_2^e_2)*(p_3^e_3)*... and min(p_1^e_1,p_2^e_2,...) = p_k^e_k then a(n) = e_k, a(1) = 0.

0, 1, 1, 2, 1, 1, 1, 3, 2, 1, 1, 1, 1, 1, 1, 4, 1, 1, 1, 2, 1, 1, 1, 1, 2, 1, 3, 2, 1, 1, 1, 5, 1, 1, 1, 2, 1, 1, 1, 1, 1, 1, 1, 2, 1, 1, 1, 1, 2, 1, 1, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 6, 1, 1, 1, 2, 1, 1, 1, 3, 1, 1, 1, 2, 1, 1, 1, 1, 4, 1, 1, 1, 1, 1, 1, 3, 1, 1, 1, 2, 1, 1, 1, 1, 1, 1, 2, 2

Offset: 1

Author

Ilya Gutkovskiy, Feb 14 2025

Keywords

• nonn

Crossrefs

Cf. A034684, A051904, A088388, A381131, A381132.

Programs

Mathematica

Table[PrimeOmega[Min @@ (#[[1]]^#[[2]] & /@ FactorInteger[n])], {n, 100}]

PARI

a(n) = if (n==1, 0, my(f=factor(n), v=vector(#f~, k, f[k,1]^f[k,2]), m=vecmin(v), i=select(x->(x==m), v, 1)); f[i[1], 2]); \\ Michel Marcus, Feb 19 2025