A225417 Composite numbers which contain their sum of aliquot parts as a substring.

6, 28, 121, 437, 496, 611, 1331, 1397, 8128, 10201, 14641, 27019, 40301, 40991, 41347, 41917, 45743, 47873, 49901, 51101, 67997, 76459, 97637, 99101, 99553, 99779, 120353, 133307, 133961, 134179, 153091, 161051, 165101, 165743, 166171, 182525, 186503

Offset: 1

Author

Antonio Roldán, May 07 2013

Keywords

• nonn
• base

Comments

A(n) is odd deficient or perfect (A000396).

If definition had not excluded prime numbers, then terms of A208270 would have been included. - Michel Marcus, Dec 18 2013

Examples

			1031311 is in the sequence because 1031311=10211*101, Sum of aliquot parts: 1+101+10211=10313, substring of 1031311.
		

Links

• Donovan Johnson, Table of n, a(n) for n = 1..1000

Programs

PARI

indigit(a,b)={ u=Vec(Str(a));v=Vec(Str(b));indi=0;la=#u;lb=#v;i=1;while(i<=la-lb+1&&indi==0,d=0;for(x=1,lb,if(v[x]==u[i+x-1],d+=1));indi=(d==lb) ;i+=1);return(indi)}
{for(i=1,10^7,k=sigma(i,1)-i;if(indigit(i,k)&&isprime(i)==0,print(i)))}