A316481
Squares whose arithmetic mean of digits is 1 (i.e., the sum of digits equals the number of digits).
Original entry on oeis.org
1, 1100401, 2220100, 100040004, 100100025, 100220121, 100400400, 101002500, 102030201, 102212100, 103002201, 104040000, 110250000, 121022001, 121220100, 123210000, 132020100, 144000000, 210221001, 225000000, 310112100, 324000000, 400040001, 400400100
Offset: 1
1049^2 = 1100401, a 7-digit number whose digit sum is 1+1+0+0+4+0+1 = 7, so 1100401 is a term.
A316484
Squares whose arithmetic mean of digits is 4 (i.e., the sum of digits is 4 times the number of digits).
Original entry on oeis.org
4, 1681, 3364, 3481, 4624, 7225, 9025, 1054729, 1069156, 1073296, 1149184, 1168561, 1183744, 1227664, 1263376, 1288225, 1308736, 1329409, 1366561, 1517824, 1522756, 1545049, 1567504, 1585081, 1607824, 1630729, 1635841, 1677025, 1682209, 1705636, 1729225
Offset: 1
1027^2 + 1054729, a 7-digit number whose digit sum is 1+0+5+4+7+2+9 = 28 = 4*7, so 1054729 is a term.
10044^2 = 100881936, a 9-digit number whose digit sum is 1+0+0+8+8+1+9+3+6 = 36 = 4*9, so 100881936 is a term.
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f:= proc(n) local L;
L:= convert(n^2,base,10);
if convert(L,`+`)=4*nops(L) then n^2 fi
end proc:
map(f, [$1..2000]); # Robert Israel, Jul 05 2018
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Select[Range[1500]^2, Mean[IntegerDigits[#]] == 4 &] (* Giovanni Resta, Jul 05 2018 *)
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isok(n) = (n>0) && issquare(n) && (sumdigits(n) == 4*#digits(n)); \\ Michel Marcus, Jul 05 2018
A316488
Squares whose arithmetic mean of digits is 8 (i.e., the sum of digits is 8 times the number of digits).
Original entry on oeis.org
97969, 88998998929, 97888999968769, 38999699989995889, 79949788888999969, 98987998979757889, 99497897999899876, 498999778899898896, 597998978979699969, 799778987996998689, 896899597989995889, 899984989899599769, 979978999994798769, 989999999787828969
Offset: 1
313^2 = 97969, a 5-digit number whose digit sum is 9+7+9+6+9 = 40 = 8*5, so 97969 is a term.
9949823114^2 = 98998979999888656996, a 20-digit number whose digit sum is 9+8+9+9+8+9+7+9+9+9+9+8+8+8+6+5+6+9+9+6 = 160 = 8*20, so 98998979999888656996 is a term.
A316482
Squares whose arithmetic mean of digits is 2 (i.e., the sum of digits is twice the number of digits).
Original entry on oeis.org
21025, 23104, 32041, 36100, 63001, 10125124, 10176100, 10233601, 10530025, 10824100, 11122225, 11303044, 11424400, 12040900, 12103441, 12222016, 12602500, 13315201, 13322500, 14055001, 14600041, 16008001, 16080100, 16810000, 20205025, 20214016, 20611600
Offset: 1
145^2 = 21025, a 5-digit number whose digit sum is 2+1+0+2+5 = 10 = 2*5, so 21025 is a term.
A316483
Squares whose arithmetic mean of digits is 3 (i.e., the sum of digits is 3 times the number of digits).
Original entry on oeis.org
144, 225, 324, 441, 900, 108900, 114921, 119025, 125316, 129600, 136161, 140625, 145161, 159201, 161604, 164025, 176400, 184041, 205209, 210681, 213444, 216225, 219024, 221841, 239121, 242064, 245025, 248004, 254016, 291600, 304704, 308025, 311364, 314721
Offset: 1
12^2 = 144, a 3-digit number whose digit sum is 1+4+4 = 9 = 3*3, so 144 is a term.
360^2 = 129600, a 6-digit number whose digit sum is 1+2+9+6+0+0 = 18 = 3*6, so 129600 is a term.
A316485
Squares whose arithmetic mean of digits is 5 (i.e., the sum of digits is 5 times the number of digits).
Original entry on oeis.org
64, 12769, 14884, 24649, 24964, 27556, 30976, 33856, 37249, 37636, 44944, 48841, 56644, 65536, 66049, 70756, 75076, 75625, 80089, 80656, 85264, 96721, 10778089, 10982596, 11464996, 11498881, 11648569, 11957764, 11992369, 12369289, 12559936, 12687844, 12909649
Offset: 1
8^2 = 64, a 2-digit number whose digit sum is 6+4 = 10 = 5*2, so 64 is a term.
3283^2 = 10778089, an 8-digit number whose digit sum is 1+0+7+7+8+0+8+9 = 40 = 5*8, so 10778089 is a term.
A316486
Squares whose arithmetic mean of digits is 6 (i.e., the sum of digits is 6 times the number of digits).
Original entry on oeis.org
576, 729, 149769, 173889, 178929, 199809, 278784, 288369, 294849, 389376, 439569, 459684, 467856, 471969, 509796, 589824, 599076, 617796, 660969, 665856, 675684, 685584, 695556, 746496, 751689, 767376, 777924, 788544, 793881, 799236, 853776, 859329, 870489
Offset: 1
24^2 = 576, a 3-digit number whose digit sum is 5+7+6 = 18 = 6*3, so 576 is a term.
10386^2 = 107868996, a 9-digit number whose digit sum is 1+0+7+8+6+8+9+9+6 = 54 = 6*9, so 107868996 is a term.
A316487
Squares whose arithmetic mean of digits is 7 (i.e., the sum of digits is 7 times the number of digits).
Original entry on oeis.org
2778889, 4695889, 5678689, 5697769, 5938969, 6568969, 6589489, 6848689, 6895876, 7974976, 7997584, 8779369, 9878449, 9966649, 299739969, 377796969, 396686889, 458687889, 467986689, 487658889, 488984769, 496977849, 538889796, 557998884, 559984896, 569967876
Offset: 1
17313^2 = 299739969, a 9-digit number whose digit sum is 2+9+9+7+3+9+9+6+9 = 63 = 7*9, so 299739969 is a term.
43474^2 = 1889988676, a 10-digit number whose digit sum is 1+8+8+9+9+8+8+6+7+6 = 70 = 7*10, so 1889988676 is a term.
Showing 1-8 of 8 results.
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