A103125 -id:A103125 - cp's OEIS frontend

A195191 Smallest n-Smith number.

32, 402, 2401, 2030, 10112, 10, 200, 10200, 10010, 100200, 1000110, 1000200, 100, 20000, 10200000, 1001000, 100200000, 1000110000, 1000200000, 1000, 2000000, 10200000000, 100100000, 100200000000, 1000110000000, 1000000000100, 10000, 200000000

Offset: 2

Kausthub Gudipati, Sep 11 2011

The smallest number for which the sum of the digits of its prime factors equals n multiplied by the sum of its digits.

			The first term of A104390, the first term of A104391, the first term of A103125 etc.

Shyam Sunder Gupta, Smith numbers

A007953 := proc(n) add(d,d=convert(n,base,10)) ; end proc:
A118503 := proc(n) a := 0 ; for p in ifactors(n)[2] do a := a+ op(2,p)*A007953(op(1,p)) ; end do: a ; end proc:
A195191 := proc(n) for k from 1 do if A118503(k) = n*A007953(k) then return k; end if; end do: end proc: # R. J. Mathar, Sep 14 2011

a(12)-a(29) from Donovan Johnson, Sep 15 2011

A385932 Composite numbers m such that the sum of digits of m divides the sum of digits of prime factors of m (counted with multiplicity).

Original entry on oeis.org

4, 10, 22, 27, 32, 42, 58, 60, 70, 85, 94, 100, 104, 121, 152, 166, 200, 202, 231, 265, 274, 315, 316, 319, 322, 330, 342, 346, 355, 361, 378, 382, 391, 402, 406, 430, 438, 450, 454, 483, 510, 517, 526, 535, 540, 562, 576, 588, 602, 610, 612, 627, 632, 634, 636, 645, 648

Offset: 1

Stefano Spezia, Jul 12 2025

Equivalently, numbers m such that A007953(m) | A118503(m).

Union of the k-Smith numbers for all the positive integers k.

			10 = 2*5 is a term since it is a 7-Smith number: 1 + 0 = 1 | 7 = 2 + 5;
60 = 2^2*3*5 is term since it is a 2-Smith number: 6 + 0 = 6 | 12 = 2 + 2 + 3 + 5;
382 = 2*191 is a term since it is a Smith number (k=1): 3 + 8 + 2 = 13 | 13 = 2 + 1 + 9 + 1;
635 = 5*127 is not a term since 6 + 3 + 5 = 14 does not divide 15 = 5 + 1 + 2 + 7.

James J. Tattersall, Elementary Number Theory in Nine Chapters, Cambridge University Press, 1999, Exercise 3.1.14 and 3.1.16 on pages 84-85.

Wayne L. McDaniel, The Existence of Infinitely Many k-Smith Numbers, The Fibonacci Quarterly, 25(1), 76-80, (1987).

Supersequence of A006753, A103125, A103126, A104390, A104391.

Cf. A002808, A007953, A118503.

fQ[n_]:=!PrimeQ[n] && n>1 && Divisible[Total[Flatten[IntegerDigits[Table[#[[1]], {#[[2]]}]] & /@ FactorInteger[n]]], Total[IntegerDigits[n]]]; Select[ Range@ 650, fQ]

cp's OEIS Frontend

A195191 Smallest n-Smith number.

Views

Author

Keywords

Comments

Examples

Links

Programs

Maple

Extensions