A357126 a(n) is the smallest positive integer k such that k > n and A071364(k) = A071364(n).

3, 5, 9, 7, 10, 11, 27, 25, 14, 13, 20, 17, 15, 21, 81, 19, 50, 23, 28, 22, 26, 29, 40, 49, 33, 125, 44, 31, 42, 37, 243, 34, 35, 38, 100, 41, 39, 46, 56, 43, 66, 47, 45, 52, 51, 53, 80, 121, 75, 55, 63, 59, 250, 57, 88, 58, 62, 61, 84, 67, 65, 68, 729, 69, 70, 71, 76, 74, 78, 73, 200, 79, 77, 98

Offset: 2

Author

Gleb Ivanov, Oct 26 2022

Keywords

• nonn

Examples

			a(12) = 20 as 12 has (2, 1) sequence of exponents in canonical prime factorization via 12 = 2^2 * 3^1 and the smallest positive integer > 12 with the same sequence of exponents in canonical prime factorization being (2, 1) is 20 as 20 = 2^2 * 5^1. - _David A. Corneth_, Oct 26 2022
		

Crossrefs

Cf. A000961, A003961, A071364, A065642, A081382, A081761.

Programs

PARI

f4(n) = my(f = factor(n)); for (i=1, #f~, f[i, 1] = prime(i)); factorback(f); \\ A071364
a(n) = my(k=n+1, f=f4(n)); while (f4(k) != f, k++); k; \\ Michel Marcus, Oct 26 2022

PARI

first(n) = { my(res = vector(n + 1), todo = n, m = Map(), u = precprime(n)); for(e = 2, logint(n, 2), u = max(u, nextprime(sqrtnint(n, e) + 2)^e) ); forfactored(i = 2, u, cs = i[2][,2]; if(mapisdefined(m, cs), ci = mapget(m, cs); if(ci <= n + 1, res[ci] = i[1]; mapput(m, cs, i[1]); todo--; if(todo <= 0, res = res[^1]; return(res) ) ) , if(i[1] <= n + 1, mapput(m, cs, i[1]) ) ) ) } \\ David A. Corneth, Oct 26 2022

Python

from sympy import factorint
to_s_exp = lambda n: tuple(i[1] for i in sorted(factorint(n).items()))
terms = []
for i in range(2, 100):
    k = i+1;t = to_s_exp(i)
    while t != to_s_exp(k):k+=1
    terms.append(k)
print(terms)

Formula

a(A000961(k)) = a(A003961(A000961(k))) for k > 1. - David A. Corneth, Oct 26 2022

a(n) >= A081761(n). - Rémy Sigrist, Feb 16 2023