A171671 -id:A171671 - cp's OEIS frontend

A171672 Numbers m with property that m^2 is not of form (k + sum of digits of k).

1, 3, 8, 11, 20, 76, 83, 86, 94, 97, 104, 110, 133, 137, 166, 173, 176, 184, 187, 194, 223, 256, 263, 264, 266, 274, 275, 277, 284, 332, 353, 356, 364, 367, 396, 403, 407, 436, 443, 454, 457, 464, 504, 533, 535, 546, 587, 623, 624, 625, 634, 637, 644, 654, 673

Offset: 1

Zak Seidov, Dec 15 2009

Amiram Eldar, Table of n, a(n) for n = 1..10000
Zak Seidov, Self squares.
Zak Seidov, A171672: n^2 is safe number.

Cf. A003052 (self or Colombian numbers), A171671 (m^2 are self numbers), A062028 (a(n) = n + sum of the digits of n), A171673 (n and n^2 are self numbers).

nn=5*10^5; list=Table[n + Total[IntegerDigits[n]],{n,nn}]; Select[Sqrt[Complement[Range[nn],list]], IntegerQ[#] &] (* Jayanta Basu, May 06 2013 *)

a(n) = sqrt(A171671(n)).

Changed the word "safe" in this entry to "self". - N. J. A. Sloane, Feb 26 2017

A171673 Numbers n with property that both n and n^2 are self numbers (A003052).

Original entry on oeis.org

1, 3, 20, 86, 97, 110, 176, 187, 266, 277, 356, 367, 457, 637, 714, 716, 727, 804, 815, 894, 984, 1087, 1177, 1267, 1357, 1436, 1537, 1614, 1616, 1627, 1704, 1715, 1884, 1985, 2077, 2235, 2257, 2516, 2694, 2784, 2885, 3045, 3135, 3315, 3326, 3337, 3414

Offset: 1

Zak Seidov, Dec 15 2009

David A. Corneth, Table of n, a(n) for n = 1..10000
Zak Seidov, A171673

Cf. A003052 (Self or Colombian numbers), A171671 (self squares), A171672 (n^2 are self squares).

nn=1.2*10^7; list=Table[n + Total[IntegerDigits[n]],{n,nn}]; se=Complement[Range[nn],list]; se1=Select[Sqrt[se],IntegerQ[#]&]; Intersection[se,se1] (* Jayanta Basu, May 06 2013 *)

Changed the word "safe" in this entry to "self". - N. J. A. Sloane, Feb 26 2017

A249044 Composite self-numbers.

Original entry on oeis.org

9, 20, 42, 64, 75, 86, 108, 110, 121, 132, 143, 154, 165, 176, 187, 198, 209, 222, 244, 255, 266, 288, 299, 310, 312, 323, 334, 345, 356, 378, 400, 411, 413, 424, 435, 446, 468, 490, 501, 512, 514, 525, 536, 558, 580, 591, 602, 615, 626, 637, 648, 670, 681, 692, 703, 714, 716, 738, 749, 760, 771, 782

Offset: 1

N. J. A. Sloane, Oct 30 2014

D. R. Kaprekar, The Mathematics of the New Self Numbers, Privately Printed, 311 Devlali Camp, Devlali, India, 1963.

Reinhard Zumkeller, Table of n, a(n) for n = 1..10000
D. R. Kaprekar, The Mathematics of the New Self Numbers [annotated and scanned]

Cf. A003052, A006378, A171671.

Cf. A002808, A010051, A062028.

a249044 n = a249044_list !! (n-1)
a249044_list = filter ((== 0) . a010051') $ tail a003052_list
-- Reinhard Zumkeller, Oct 31 2014

A382166 Self-numbers (A003052) that are cubes.

Original entry on oeis.org

1, 64, 512, 1728, 35937, 50653, 195112, 287496, 300763, 314432, 681472, 804357, 884736, 1000000, 2248091, 2744000, 3241792, 4173281, 4913000, 5929741, 6434856, 6859000, 10077696, 10360232, 12167000, 13481272, 15813251, 18399744, 19902511, 22188041, 27270901, 29791000, 36264691, 37933056, 47045881

Offset: 1

N. J. A. Sloane, Mar 26 2025

Amiram Eldar, Table of n, a(n) for n = 1..10000
Shyam Sunder Gupta, On Some Marvellous Numbers of Kaprekar, Exploring the Beauty of Fascinating Numbers, Springer (2025) Ch. 9, 275-315. See Section 9.7.3.

Intersection of A000578 and A003052.

Cf. A171671.

cp's OEIS Frontend

A171672 Numbers m with property that m^2 is not of form (k + sum of digits of k).

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A171673 Numbers n with property that both n and n^2 are self numbers (A003052).

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A249044 Composite self-numbers.

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A382166 Self-numbers (A003052) that are cubes.

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