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A217747
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Numbers whose digits sum to a perfect number.
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0
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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
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OFFSET
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1,1
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COMMENTS
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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.
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LINKS
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EXAMPLE
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a(4)=33, because 3+3 is the perfect number 6.
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MATHEMATICA
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Select[Range[1500], MemberQ[{6, 28, 496, 8128}, Total[IntegerDigits[#]]]&] (* Harvey P. Dale, Mar 14 2023 *)
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PROG
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(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}
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CROSSREFS
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KEYWORD
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nonn,base
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AUTHOR
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STATUS
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approved
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