A381215 -id:A381215 - cp's OEIS frontend

A381214 a(n) is the difference between the largest and smallest element of the set of bases and exponents (including exponents = 1) in the prime factorization of n.

1, 2, 0, 4, 2, 6, 1, 1, 4, 10, 2, 12, 6, 4, 2, 16, 2, 18, 4, 6, 10, 22, 2, 3, 12, 0, 6, 28, 4, 30, 3, 10, 16, 6, 1, 36, 18, 12, 4, 40, 6, 42, 10, 4, 22, 46, 3, 5, 4, 16, 12, 52, 2, 10, 6, 18, 28, 58, 4, 60, 30, 6, 4, 12, 10, 66, 16, 22, 6, 70, 1, 72, 36, 4, 18

Offset: 2

Paolo Xausa, Feb 19 2025

			a(36) = 1 because 36 = 2^2*3^2, the set of these bases and exponents is {2, 3} and 3 - 2 = 1.
a(31500) = 6 because 31500 = 2^2*3^2*5^3*7^1, the set of these bases and exponents is {1, 2, 3, 5, 7} and 7 - 1 = 6.

Paolo Xausa, Table of n, a(n) for n = 2..10000

Cf. A046665, A081812, A381212.

Cf. A051674 (positions of zeros), A381215 (positions of ones).

A381214[n_] := Max[#] - Min[#] & [Flatten[FactorInteger[n]]];
Array[A381214, 100, 2]

a(n) = my(f=factor(n), s=setunion(Set(f[,1]), Set(f[,2]))); vecmax(s) - vecmin(s); \\ Michel Marcus, Feb 20 2025

a(n) = A081812(n) - A381212(n).

A381317 Numbers of the form p^(p +- 1), where p is prime.

Original entry on oeis.org

2, 8, 9, 81, 625, 15625, 117649, 5764801, 25937424601, 3138428376721, 23298085122481, 3937376385699289, 48661191875666868481, 14063084452067724991009, 104127350297911241532841, 37589973457545958193355601, 907846434775996175406740561329, 480250763996501976790165756943041

Offset: 1

Paolo Xausa, Feb 20 2025

Paolo Xausa, Table of n, a(n) for n = 1..150

Union of A036878 and A104126.

Subsequence of A381215.

Flatten[Map[#^{# - 1, # + 1} &, Prime[Range[10]]]]

cp's OEIS Frontend

A381214 a(n) is the difference between the largest and smallest element of the set of bases and exponents (including exponents = 1) in the prime factorization of n.

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