A362954 -id:A362954 - cp's OEIS frontend

A362953 Numbers N such that N + the sum of the cubes of its digits is again a third power.

0, 34, 352, 540, 1167, 1942, 2176, 3312, 4093, 5454, 8019, 9380, 12025, 12130, 13068, 13158, 15344, 15991, 16279, 16675, 21149, 22699, 22789, 30988, 32257, 32365, 35238, 37883, 37955, 41866, 45549, 54523, 57906, 58530, 62579, 72588, 83692, 83782, 89604, 102952

Offset: 0

Will Gosnell and M. F. Hasler, May 09 2023

			The sum of the cubes of the digits of N = 34 is 3^3 + 4^3 = 27 + 64 = 91; added to the number N itself yields  125 which is again a cube, 5^3. Therefore 34 is in this sequence.

Karl-Heinz Hofmann, Table of n, a(n) for n = 0..10000
Karl-Heinz Hofmann, Visualization of n = 0 to 11.

Cf. A000578 (the cubes), A055012 (sum of cubes of decimal digits of n).

Cf. A362954 (the same for 4th powers).

select( {is(n,p=3)=ispower(vecsum([d^p|d<-digits(n)])+n,p)}, [0..10^5])

aupto = 103000
A362953 = []
A000578 = set(cu**3 for cu in range(0, int(aupto**(1/3)+3)))
for n in range(0,aupto+1):
    if n + sum(int(digit)**3 for digit in str(n)) in A000578: A362953.append(n)
print(A362953) # Karl-Heinz Hofmann, May 24 2023

A362945 Numbers k such that k + the sum of the fifth powers of its digits is again a fifth power.

Original entry on oeis.org

0, 210, 66374, 76933, 294137, 722571, 741300, 1023716, 2412593, 3959235, 4022940, 5090402, 6351886, 7821198, 9653864, 11808061, 11814811, 20427955, 24190287, 24239133, 24245187, 33518020, 33532714, 33536551, 39060306, 52476271, 52480534, 69255266, 69265142, 79091461, 89980491, 90147222

Offset: 0

M. F. Hasler, Jun 15 2023

Cf. A000584 (4th powers), A055014 (sum of 5th powers of decimal digits).

Cf. A362953 (same for 3rd powers), A362954 (same for 4th powers).

is_A362945(n,p=5)=ispower(vecsum([d^p|d<-digits(n)])+n,p)
for(n=0,1e8, is_A362945(n) && print1(n", "))

ispower5 = lambda n: n==round(n**.2)**5
is_A362945 = lambda n: ispower5(sum(int(d)**5 for d in str(n))+n)
def A362945(n, A=[0]):
    while len(A) < n:
        A.append(A[-1]+1)
        while not is_A362945(A[-1]): A[-1]+=1
    return A[n]

cp's OEIS Frontend

A362953 Numbers N such that N + the sum of the cubes of its digits is again a third power.

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