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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.
0
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
1,1
FORMULA
{ k : A007953(k) = A008474(k) }.
EXAMPLE
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.
MATHEMATICA
Select[Range[34000], DigitSum[#]==Total[Flatten[FactorInteger[#]]] &] (* Stefano Spezia, Sep 14 2024 *)
PROG
(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
(PARI) isok(k)={my(f=factor(k)); vecsum(f[, 1]) + vecsum(f[, 2]) == sumdigits(k)} \\ Andrew Howroyd, Sep 26 2024
CROSSREFS
KEYWORD
nonn,base
AUTHOR
Jordan Brooks, Sep 12 2024
STATUS
approved