A115895 -id:A115895 - cp's OEIS frontend

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

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

A115897 Numbers k such that sigma(k) + phi(k) is a palindrome.

Original entry on oeis.org

1, 2, 3, 4, 10, 11, 21, 49, 92, 101, 115, 131, 145, 186, 200, 201, 206, 207, 221, 226, 227, 240, 272, 302, 310, 313, 327, 342, 344, 370, 374, 388, 403, 406, 409, 413, 419, 425, 439, 449, 880, 948, 1015, 1055, 1132, 1165, 1385, 1443, 1680, 1755, 1785

Offset: 1

Giovanni Resta, Feb 06 2006

			sigma(1055) + phi(1055) = 1272 + 840 = 2112.

Michael De Vlieger, Table of n, a(n) for n = 1..5000

Cf. A115895, A115896.

Select[Range@ 1800, Reverse@ # == # &@ IntegerDigits[DivisorSigma[1, #] + EulerPhi@ #] &] (* Michael De Vlieger, Jul 22 2016 *)
Select[Range[2000],PalindromeQ[DivisorSigma[1,#]+EulerPhi[#]]&] (* Requires Mathematica version 10 or later *) (* Harvey P. Dale, Mar 29 2020 *)

ispal(n)=n=digits(n); Vecrev(n)==n
is(n,f=factor(n))=ispal(sigma(f)+eulerphi(f)) \\ Charles R Greathouse IV, Jul 22 2016

A115898 Numbers k such that sigma(k) + prime(k) is a palindrome.

Original entry on oeis.org

1, 2, 3, 13, 17, 36, 56, 78, 80, 83, 86, 119, 135, 178, 185, 226, 227, 235, 378, 422, 443, 579, 629, 651, 910, 1230, 1277, 1331, 1344, 1432, 1644, 1734, 1740, 1758, 1772, 1794, 1827, 1847, 1973, 2021, 2730, 2874, 2878, 2979, 2981, 3169, 3229

Offset: 1

Giovanni Resta, Feb 06 2006

			sigma(1344) + prime(1344) = 4064 + 11087 = 15151.

Cf. A115895, A115899.

A115900 Numbers k such that k + sigma(k) and k + phi(k) are palindromes.

Original entry on oeis.org

1, 2, 3, 4, 5, 219, 322, 375, 22248, 32065, 47827, 1406744, 2144055, 2991368, 3626587, 4909369, 172133971, 177457001, 328030055, 3128669654, 8345867631, 19649249526, 45179367929, 47228405729, 48534773039, 49583585599, 2127577449846, 2191781701563, 3972961263797

Offset: 1

Giovanni Resta, Feb 06 2006

Intersection of A115895 and A115896.
a(27) > 10^11. 3972961263797 is also a term. - Donovan Johnson, May 31 2013
a(30) > 10^13. - Giovanni Resta, Jun 05 2013

			4909369 + sigma(4909369) = 9823289 and 4909369 + phi(4909369) = 9814189.

Cf. A115895, A115896.

a(17)-a(26) from Donovan Johnson, Oct 05 2010

a(27)-a(29) from Giovanni Resta, Jun 05 2013

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

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A115897 Numbers k such that sigma(k) + phi(k) is a palindrome.

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A115898 Numbers k such that sigma(k) + prime(k) is a palindrome.

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A115900 Numbers k such that k + sigma(k) and k + phi(k) are palindromes.

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