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