A336965 -id:A336965 - cp's OEIS frontend

A381201 a(n) is the product of the elements of the set of bases and exponents in the prime factorization of n.

1, 2, 3, 2, 5, 6, 7, 6, 6, 10, 11, 6, 13, 14, 15, 8, 17, 6, 19, 10, 21, 22, 23, 6, 10, 26, 3, 14, 29, 30, 31, 10, 33, 34, 35, 6, 37, 38, 39, 30, 41, 42, 43, 22, 30, 46, 47, 24, 14, 10, 51, 26, 53, 6, 55, 42, 57, 58, 59, 30, 61, 62, 42, 12, 65, 66, 67, 34, 69, 70

Offset: 1

Paolo Xausa, Feb 16 2025

The prime factorization of 1 is the empty set, so a(1) = 1 by convention (empty product).

			a(12) = 6 because 12 = 2^2*3^1, the set of these bases and exponents is {1, 2, 3} and 1*2*3 = 6.
a(31500) = 210 because 31500 = 2^2*3^2*5^3*7^1, the set of these bases and exponents is {1, 2, 3, 5, 7} and 1*2*3*5*7 = 210.

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

Cf. A000026, A336965, A381202, A381203, A381204, A381205.

A381201[n_] := Times @@ Union[Flatten[FactorInteger[n]]];
Array[A381201, 100]

a(n) = my(f=factor(n)); vecprod(Vec(setunion(Set(f[,1]), Set(f[,2])))); \\ Michel Marcus, Feb 18 2025

A336964 Irregular triangle in which first row is 1, n-th row (n > 1) lists distinct prime numbers in the prime tower factorization of n.

Original entry on oeis.org

1, 2, 3, 2, 5, 2, 3, 7, 2, 3, 2, 3, 2, 5, 11, 2, 3, 13, 2, 7, 3, 5, 2, 17, 2, 3, 19, 2, 5, 3, 7, 2, 11, 23, 2, 3, 2, 5, 2, 13, 3, 2, 7, 29, 2, 3, 5, 31, 2, 5, 3, 11, 2, 17, 5, 7, 2, 3, 37, 2, 19, 3, 13, 2, 3, 5, 41, 2, 3, 7, 43, 2, 11, 2, 3, 5, 2, 23, 47, 2, 3

Offset: 1

Rémy Sigrist, Aug 09 2020

The prime tower factorization of a number is defined in A182318.

The n-th row includes the n-th row of A027748.

			Triangle begins:
     1    [1]
     2    [2]
     3    [3]
     4    [2]
     5    [5]
     6    [2, 3]
     7    [7]
     8    [2, 3]
     9    [2, 3]
    10    [2, 5]
    11    [11]
    12    [2, 3]
    13    [13]
    14    [2, 7]
    15    [3, 5]

Rémy Sigrist, Table of n, a(n) for n = 1..10001 (rows for n = 1..4045)

Cf. A027748, A115588 (row lengths), A182318, A336965.

row(n) = { my (f=factor(n), p=f[,1]~); for (k=1, #f~, if (f[k,2]>1, p=concat(p, row(f[k,2])));); if (#p==0, [1], Set(p)) }

cp's OEIS Frontend

A381201 a(n) is the product of the elements of the set of bases and exponents in the prime factorization of n.

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