A381131 -id:A381131 - cp's OEIS frontend

A381132 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) = pi(p_k), a(1) = 0.

0, 1, 2, 1, 3, 1, 4, 1, 2, 1, 5, 2, 6, 1, 2, 1, 7, 1, 8, 1, 2, 1, 9, 2, 3, 1, 2, 1, 10, 1, 11, 1, 2, 1, 3, 1, 12, 1, 2, 3, 13, 1, 14, 1, 3, 1, 15, 2, 4, 1, 2, 1, 16, 1, 3, 4, 2, 1, 17, 2, 18, 1, 4, 1, 3, 1, 19, 1, 2, 1, 20, 1, 21, 1, 2, 1, 4, 1, 22, 3

Offset: 1

Ilya Gutkovskiy, Feb 14 2025

nonn

Cf. A000720, A034684, A055396, A108230, A381131, A381133.

Table[PrimePi[Exp[MangoldtLambda[Min @@ (#[[1]]^#[[2]] & /@ FactorInteger[n])]]], {n, 80}]

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)); primepi(f[i[1], 1])); \\ Michel Marcus, Feb 19 2025

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.

Original entry on oeis.org

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

Ilya Gutkovskiy, Feb 14 2025

nonn

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

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

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

cp's OEIS Frontend

A381132 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) = pi(p_k), a(1) = 0.

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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.

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cp's OEIS Frontend

A381132 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) = pi(p_k), a(1) = 0.

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PARI

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.

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Mathematica

PARI

A381132 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) = pi(p_k), a(1) = 0.

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.