A132628 Numbers n for which the sum of their digits divides sigma(n).

1, 6, 10, 11, 15, 19, 20, 22, 24, 30, 31, 33, 35, 42, 51, 52, 60, 62, 66, 68, 71, 79, 87, 90, 100, 101, 102, 103, 104, 105, 109, 110, 112, 114, 118, 120, 123, 124, 130, 132, 136, 138, 141, 143, 145, 147, 150, 153, 160, 161, 165, 167, 168, 174, 177, 190, 194, 198

Offset: 1

Author

Paolo P. Lava and Giorgio Balzarotti, Aug 24 2007

Keywords

• nonn
• base
• easy

Examples

			n=147 -> sigma(n)=1+3+7+21+49+147=228 Sum_digits(n)=1+4+7=12 -> 228/12 = 19
n=177 -> sigma(n)=1+3+59+177=240 Sum_digits(n)=1+7+7=15 -> 240/15 = 16
		

Links

• Harvey P. Dale, Table of n, a(n) for n = 1..1000

Crossrefs

Cf. A007691, A054030, A132629.

Programs

Maple

with(numtheory); P:=proc(n) local a,i,j,k,w; for i from 1 by 1 to n do w:=0; k:=i; while k>0 do w:=w+k-(trunc(k/10)*10); k:=trunc(k/10); od; j:=sigma(i)/w; if trunc(j)=j then print(i,j); fi; od; end: P(200)

Mathematica

Select[Range[200],Divisible[DivisorSigma[1,#],Total[IntegerDigits[#]]]&] (* Harvey P. Dale, Dec 06 2012 *)