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

1,1

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.

Links

Table of n, a(n) for n=1..49.

Example

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

Mathematica

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

Prog

(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}

Crossrefs

Cf. A052220, A007953, A000396.

Superset of A048517

Sequence in context: A017233 A122709 A052220 * A341007 A345959 A242405

Adjacent sequences: A217744 A217745 A217746 * A217748 A217749 A217750

Keyword

nonn,base

Author

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

Status

approved