A174460 Smith numbers of order 2.

56, 58, 810, 822, 1075, 1519, 1752, 2145, 2227, 2260, 2483, 2618, 2620, 3078, 3576, 3653, 3962, 4336, 4823, 4974, 5216, 5242, 5386, 5636, 5719, 5762, 5935, 5998, 6220, 6424, 6622, 6845, 7015, 7251, 7339, 7705, 7756, 8460, 9254, 9303, 9355, 10481, 10626, 10659

Offset

1,1

Comments

Composite numbers a(n) such that the sum of digits^2 equals the sum of digits^2 of its prime factors without the numbers of A176670 that have the same digits as its prime factors (without the zero digit).

It seems as though as the order n approaches infinity, the sequence of n-order Smith numbers approaches A176670. Is there a value of n where the only n-order Smith numbers are members of A176670? - Ely Golden, Dec 07 2016

Links

Ely Golden and Donovan Johnson, Table of n, a(n) for n = 1..10000 (terms 1 to 1000 by Donovan Johnson)

Patrick Costello, A new largest Smith number, Fibonacci Quarterly 40(4) (2002), 369-371.

Underwood Dudley, Smith numbers, Mathematics Magazine 67(1) (1994), 62-65.

Ely Golden, Smith number sequence generator optimized for order 2.

S. S. Gupta, Smith Numbers, Mathematical Spectrum 37(1) (2004/5), 27-29.

S. S. Gupta, Smith Numbers.

Eric Weisstein's World of Mathematics, Smith number.

Wikipedia, Smith number.

A. Wilansky, Smith Numbers, Two-Year College Math. J. 13(1) (1982), p. 21.

Amin Witno, Another simple construction of Smith numbers, Missouri J. Math. Sci. 22(2) (2010), 97-101.

Amin Witno, Smith multiples of a class of primes with small digital sum, Thai Journal of Mathematics 14(2) (2016), 491-495.

Example

a(2) = 58 = 2*29 is a Smith number of order 2 because 5^2 + 8^2 = 2^2 + 2^2 + 9^2 = 89.

Maple

for s from 2 to 10000 do g:=nops(ifactors(s)[2]): qsp:=0: for u from 1 to g do z:=ifactors(s)[2, u][1]: h:=0: while (z>0) do z:=iquo(z, 10, 'r'): h:=h+r^2: end do: h:=h*ifactors(s)[2, u][2]: qsp:=qsp+h: end do: z:=s: qs:=0: while (z>0) do z:=iquo(z, 10, 'r'): qs:=qs+r^2: end do: if (qsp=qs) then print(s): end if: end do:

Mathematica

With[{k = 2}, Select[Range[12000], Function[n, And[Total@ Map[#^k &, IntegerDigits@ n] == Total@ Map[#^k &, Flatten@ IntegerDigits[#]], Not[Sort@ DeleteCases[#, 0] &@ IntegerDigits@ n == Sort@ DeleteCases[#, 0] &@ #]] &@ Flatten@ Map[IntegerDigits@ ConstantArray[#1, #2] & @@ # &, FactorInteger@ n]]]] (* Michael De Vlieger, Dec 10 2016 *)

Crossrefs

Cf. A006753 (Smith numbers), A176670, A178213, A178193, A178203, A178204.

Sequence in context: A003897 A345493 A031319 * A345494 A345495 A045001

Adjacent sequences: A174457 A174458 A174459 * A174461 A174462 A174463

Keyword

nonn,base

Author

Paul Weisenhorn, Dec 20 2010

Status

approved