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

Author

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

Keywords

• nonn
• base

Examples

			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.
		

Links

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

Crossrefs

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

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

Programs

PARI

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

Python

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