A376157 Numbers k such that the sum of the digits of k equals the sum of its prime factors plus the sum of the multiplicities of each prime factor.

4, 25, 36, 54, 125, 192, 289, 297, 343, 392, 448, 676, 756, 1089, 1536, 1764, 1936, 2646, 2888, 3872, 4802, 4860, 6174, 6250, 6776, 6860, 7290, 7488, 7680, 8750, 8775, 9408, 9747, 10648, 14739, 15309, 16848, 18432, 18865, 21296, 22869, 25725, 29988, 33750, 33957

Offset: 1

Author

Jordan Brooks, Sep 12 2024

Keywords

• nonn
• base

Examples

			For k = 54, its prime factorization is 2^1*3^3: 5+4 = 2+1+3+3 = 9.
For k = 756, its prime factorization is 2^2*3^3*7^1: 7+5+6 = 2+2+3+3+7+1 = 18.
		

Crossrefs

Similar to A006753, A019506, A050689, A063737, A070275, A285494.

Cf. A007953, A008474.

Programs

Mathematica

Select[Range[34000], DigitSum[#]==Total[Flatten[FactorInteger[#]]] &] (* Stefano Spezia, Sep 14 2024 *)

PARI

isok(k)={my(f=factor(k)); vecsum(f[,1]) + vecsum(f[,2]) == sumdigits(k)} \\ Andrew Howroyd, Sep 26 2024

Python

from sympy.ntheory import factorint
c = 2
while c < 10000:
    charsum = 0
    for char in str(c):
        charsum += int(char)
    pf = factorint(c)
    cand = 0
    for p in pf.keys():
        cand += p
        cand += pf[p]
    if charsum == cand:
        print(c)
        print(pf)
    c += 1

Formula

{ k : A007953(k) = A008474(k) }.