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

22, 58, 84, 85, 94, 136, 160, 166, 202, 234, 250, 265, 274, 308, 319, 336, 346, 355, 361, 364, 382, 391, 424, 438, 454, 456, 476, 483, 516, 517, 526, 535, 562, 627, 634, 644, 645, 650, 654, 660, 663, 690, 702, 706, 732, 735, 762, 778, 855, 860

Offset: 1

Author

Mario Velucchi (mathchess(AT)velucchi.it)

Keywords

• nonn
• base

Examples

			22 = 2*11 and digit-sum(22) = 4 = digit-sum(2) + digit-sum(11).
		

Links

• Reinhard Zumkeller, Table of n, a(n) for n = 1..10000
• Shyam Sunder Gupta, Smith Numbers, Exploring the Beauty of Fascinating Numbers, Springer (2025) Ch. 4, 127-157.
• Eric Weisstein's World of Mathematics, Hoax Number

Crossrefs

Cf. A006753.

Cf. A002808, A027748, A001221, A007953, A050223, A202393, A202387.

Programs

Haskell

a019506 n = a019506_list !! (n-1)
a019506_list = [x | x <- a002808_list,
                    a007953 x == sum (map a007953 (a027748_row x))]
-- Reinhard Zumkeller, Dec 19 2011

Mathematica

Select[Range[2,1000],!PrimeQ[#]&&Total[Flatten[IntegerDigits/@ Transpose[ FactorInteger[#]][[1]]]]==Total[IntegerDigits[#]]&] (* Harvey P. Dale, Feb 24 2013 *)

PARI

isok(m) = !isprime(m) && (sumdigits(m) == vecsum(apply(sumdigits, factor(m)[,1]))); \\ Michel Marcus, Feb 03 2022

Formula

A007953(a(n)) = sum(A007953(A027748(a(n),k)): k=1..A001221(a(n))) and A066247(a(n)) = 1. [Reinhard Zumkeller, Dec 19 2011]