A115897 -id:A115897 - cp's OEIS frontend

A115895 Numbers k such that k + sigma(k) is a palindrome.

1, 2, 3, 4, 5, 9, 34, 64, 81, 128, 141, 148, 151, 161, 162, 170, 181, 191, 196, 198, 219, 236, 249, 256, 257, 260, 277, 282, 297, 315, 322, 326, 327, 334, 346, 353, 355, 358, 373, 375, 377, 383, 387, 415, 473, 479, 499, 714, 793, 1225, 1316, 1420, 1517, 1593

Offset: 1

Giovanni Resta, Feb 06 2006

			128 + sigma(128) = 128 + 255 = 383.

Harvey P. Dale, Table of n, a(n) for n = 1..1000

Cf. A115890, A115896, A115897.

Select[Range[1600],PalindromeQ[#+DivisorSigma[1,#]]&] (* Requires Mathematica version 10 or later *) (* Harvey P. Dale, May 29 2017 *)

A115896 Numbers k such that k + phi(k) is a palindrome.

Original entry on oeis.org

1, 2, 3, 4, 5, 6, 17, 21, 61, 63, 71, 142, 157, 167, 183, 184, 190, 197, 201, 213, 215, 219, 237, 255, 263, 283, 284, 293, 305, 322, 325, 338, 359, 375, 379, 389, 395, 407, 412, 427, 445, 452, 458, 459, 460, 483, 535, 539, 549, 566, 568, 586, 595, 603, 941

Offset: 1

Giovanni Resta, Feb 06 2006

			183 + phi(183) = 183 + 120 = 303.

Robert Israel, Table of n, a(n) for n = 1..1000

Cf. A115890, A115895, A115897.

Cf. A121048 (n+phi(n)).

ispali:= proc(n) local L; L:= convert(n,base,10); andmap(t -> L[t]=L[-t], [$1..nops(L)/2]) end proc:
select(t -> ispali(t+numtheory:-phi(t)), [$1..1000]); # Robert Israel, Sep 19 2022

nppQ[n_]:=Module[{idn=IntegerDigits[n+EulerPhi[n]]},idn==Reverse[idn]]; Select[Range[1000],nppQ] (* Harvey P. Dale, Aug 18 2013 *)

ispal(n) = my(d=digits(n)); d == Vecrev(d) \\ A002113
isok(k) = ispal(k+eulerphi(k)) \\ Alexandru Petrescu, Sep 19 2022

A116030 sigma(n) - phi(n) is a palindrome greater than 2.

Original entry on oeis.org

4, 8, 9, 18, 25, 27, 28, 57, 62, 72, 85, 123, 128, 176, 184, 189, 192, 218, 220, 234, 243, 246, 252, 256, 258, 259, 261, 278, 282, 306, 309, 316, 322, 332, 338, 339, 356, 375, 380, 388, 399, 403, 490, 495, 505, 512, 518, 544, 590, 597, 622, 632, 655, 662

Offset: 1

Giovanni Resta, Feb 13 2006

When n is prime sigma(n)-phi(n) is 2, so that case is trivial.

			sigma(399) - phi(399) = 424.

Harvey P. Dale, Table of n, a(n) for n = 1..1000

Cf. A115897, A116031.

[n: n in [1..1000] | Intseq(d) eq Reverse(Intseq(d)) and d gt 2 where d is DivisorSigma(1,n)-EulerPhi(n)]; // Bruno Berselli, Sep 09 2015

pg2Q[n_]:=With[{c=DivisorSigma[1,n]-EulerPhi[n]},PalindromeQ[c]&&c>2]; Select[ Range[700],pg2Q] (* Harvey P. Dale, Jan 16 2023 *)

A116031 sigma(n)-phi(n) and sigma(n)+phi(n) are two palindromes greater than 2.

Original entry on oeis.org

4, 388, 403, 10010, 11481, 12215, 41242, 42173, 44243, 223261, 223487, 403303, 2302031, 3288877, 3490447, 32605627, 40077553, 40162802, 42311323, 44044043, 117426509, 222613051, 230777581, 232075811, 287772226, 307222207, 327067459

Offset: 1

Giovanni Resta, Feb 13 2006

			sigma(3288877)-phi(3288877) = 44444 and
sigma(3288877)+phi(3288877)=6577756.

Cf. A115897, A116030.

a(15)-a(27) from Donovan Johnson, Feb 05 2010

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A115895 Numbers k such that k + sigma(k) is a palindrome.

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A115896 Numbers k such that k + phi(k) is a palindrome.

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A116030 sigma(n) - phi(n) is a palindrome greater than 2.

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A116031 sigma(n)-phi(n) and sigma(n)+phi(n) are two palindromes greater than 2.

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