cp's OEIS Frontend

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.

%I A376157 #27 Sep 30 2024 12:58:28
%S A376157 4,25,36,54,125,192,289,297,343,392,448,676,756,1089,1536,1764,1936,
%T A376157 2646,2888,3872,4802,4860,6174,6250,6776,6860,7290,7488,7680,8750,
%U A376157 8775,9408,9747,10648,14739,15309,16848,18432,18865,21296,22869,25725,29988,33750,33957
%N 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.
%F A376157 { k : A007953(k) = A008474(k) }.
%e A376157 For k = 54, its prime factorization is 2^1*3^3: 5+4 = 2+1+3+3 = 9.
%e A376157 For k = 756, its prime factorization is 2^2*3^3*7^1: 7+5+6 = 2+2+3+3+7+1 = 18.
%t A376157 Select[Range[34000], DigitSum[#]==Total[Flatten[FactorInteger[#]]] &] (* _Stefano Spezia_, Sep 14 2024 *)
%o A376157 (Python)
%o A376157 from sympy.ntheory import factorint
%o A376157 c = 2
%o A376157 while c < 10000:
%o A376157     charsum = 0
%o A376157     for char in str(c):
%o A376157         charsum += int(char)
%o A376157     pf = factorint(c)
%o A376157     cand = 0
%o A376157     for p in pf.keys():
%o A376157         cand += p
%o A376157         cand += pf[p]
%o A376157     if charsum == cand:
%o A376157         print(c)
%o A376157         print(pf)
%o A376157     c += 1
%o A376157 (PARI) isok(k)={my(f=factor(k)); vecsum(f[,1]) + vecsum(f[,2]) == sumdigits(k)} \\ _Andrew Howroyd_, Sep 26 2024
%Y A376157 Similar to A006753, A019506, A050689, A063737, A070275, A285494.
%Y A376157 Cf. A007953, A008474.
%K A376157 nonn,base
%O A376157 1,1
%A A376157 _Jordan Brooks_, Sep 12 2024