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A019506 Hoax numbers: composite numbers whose digit-sum equals the sum of the digit-sums of its distinct prime factors.

%I A019506 #27 Mar 13 2025 11:17:57
%S A019506 22,58,84,85,94,136,160,166,202,234,250,265,274,308,319,336,346,355,
%T A019506 361,364,382,391,424,438,454,456,476,483,516,517,526,535,562,627,634,
%U A019506 644,645,650,654,660,663,690,702,706,732,735,762,778,855,860
%N A019506 Hoax numbers: composite numbers whose digit-sum equals the sum of the digit-sums of its distinct prime factors.
%H A019506 Reinhard Zumkeller, <a href="/A019506/b019506.txt">Table of n, a(n) for n = 1..10000</a>
%H A019506 Shyam Sunder Gupta, <a href="https://doi.org/10.1007/978-981-97-2465-9_4">Smith Numbers</a>, Exploring the Beauty of Fascinating Numbers, Springer (2025) Ch. 4, 127-157.
%H A019506 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/HoaxNumber.html">Hoax Number</a>
%F A019506 A007953(a(n)) = sum(A007953(A027748(a(n),k)): k=1..A001221(a(n))) and A066247(a(n)) = 1. [_Reinhard Zumkeller_, Dec 19 2011]
%e A019506 22 = 2*11 and digit-sum(22) = 4 = digit-sum(2) + digit-sum(11).
%t A019506 Select[Range[2,1000],!PrimeQ[#]&&Total[Flatten[IntegerDigits/@ Transpose[ FactorInteger[#]][[1]]]]==Total[IntegerDigits[#]]&] (* _Harvey P. Dale_, Feb 24 2013 *)
%o A019506 (Haskell)
%o A019506 a019506 n = a019506_list !! (n-1)
%o A019506 a019506_list = [x | x <- a002808_list,
%o A019506                     a007953 x == sum (map a007953 (a027748_row x))]
%o A019506 -- _Reinhard Zumkeller_, Dec 19 2011
%o A019506 (PARI) isok(m) = !isprime(m) && (sumdigits(m) == vecsum(apply(sumdigits, factor(m)[,1]))); \\ _Michel Marcus_, Feb 03 2022
%Y A019506 Cf. A006753.
%Y A019506 Cf. A002808, A027748, A001221, A007953, A050223, A202393, A202387.
%K A019506 nonn,base
%O A019506 1,1
%A A019506 Mario Velucchi (mathchess(AT)velucchi.it)