A217747 Numbers whose digits sum to a perfect number.

6, 15, 24, 33, 42, 51, 60, 105, 114, 123, 132, 141, 150, 204, 213, 222, 231, 240, 303, 312, 321, 330, 402, 411, 420, 501, 510, 600, 1005, 1014, 1023, 1032, 1041, 1050, 1104, 1113, 1122, 1131, 1140, 1203, 1212, 1221, 1230, 1302, 1311, 1320, 1401, 1410, 1500

Offset: 1

Author

Kevin L. Schwartz and Christian N. K. Anderson, Mar 23 2013

Keywords

• nonn
• base

Comments

This is the index of numbers in A007953 whose value is found in A000396.

The first 49 terms of this sequence sum to 6 (A052220). The first divergence is a(50)=1999; lengthy divergences occur for 131 consecutive values starting with a(120)=6499, and 248 consecutive values starting with a(595)=24499.

Examples

			a(4)=33, because 3+3 is the perfect number 6.
		

Crossrefs

Cf. A052220, A007953, A000396.

Superset of A048517

Programs

Mathematica

Select[Range[1500],MemberQ[{6,28,496,8128},Total[IntegerDigits[#]]]&] (* Harvey P. Dale, Mar 14 2023 *)

R

perf=c(6, 28, 496, 8128, 33550336, 8589869056, 137438691328, 2305843008139952128); i=6; psod=c(); while(length(psod)<1000) {x=which(sumod(i)==perf); if(length(x)) psod=c(psod,i+x/10); i=i+1}