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

1,1

Links

Reinhard Zumkeller, Table of n, a(n) for n = 1..10000

Eric Weisstein's World of Mathematics, Hoax Number

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]

Example

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

Mathematica

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

Prog

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

Crossrefs

Cf. A006753.

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

Sequence in context: A088820 A058097 A131878 * A202387 A044124 A044505

Adjacent sequences: A019503 A019504 A019505 * A019507 A019508 A019509

Keyword

nonn,base

Author

Mario Velucchi (mathchess(AT)velucchi.it)

Status

approved