cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

Showing 1-5 of 5 results.

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

Original entry on oeis.org

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

Views

Author

Giovanni Resta, Feb 06 2006

Keywords

Examples

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

Links

Crossrefs

Cf. A115890, A115896, A115897.

Programs

  • Mathematica
    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

Views

Author

Giovanni Resta, Feb 06 2006

Keywords

Examples

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

Links

Crossrefs

Cf. A115890, A115895, A115897.
Cf. A121048 (n+phi(n)).

Programs

  • Maple
    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
  • Mathematica
    nppQ[n_]:=Module[{idn=IntegerDigits[n+EulerPhi[n]]},idn==Reverse[idn]]; Select[Range[1000],nppQ] (* Harvey P. Dale, Aug 18 2013 *)
  • PARI
    ispal(n) = my(d=digits(n)); d == Vecrev(d) \\ A002113
isok(k) = ispal(k+eulerphi(k)) \\ Alexandru Petrescu, Sep 19 2022

A115891 Numbers k such that k times phi(k) is a palindrome.

Original entry on oeis.org

1, 2, 3, 4, 17, 21, 206, 296, 309, 314, 392, 412, 444, 3016, 3074, 3182, 3552, 3632, 4944, 12998, 52009, 296448, 2306507, 2343809, 2958948, 3842106, 4419666, 14697047, 15137567, 21150749, 25829523, 29916818, 41798278, 157946358, 215882549, 318635303, 442991424
Offset: 1

Views

Author

Giovanni Resta, Feb 06 2006

Keywords

Examples

			25829523 * phi(25829523) = 25829523 * 17219628 = 444774777477444.

Crossrefs

Cf. A084122, A115890, A115892.

Extensions

a(34)-a(37) from Donovan Johnson, Feb 17 2013

A115892 Numbers k such that sigma(k)*phi(k) is a palindrome.

Original entry on oeis.org

1, 2, 3, 69, 219, 221, 224, 254, 1772, 2181, 15463, 50807, 63551, 94236, 161257, 602962, 2105689, 8371756, 2115856505, 2539027806, 5472276593, 6819131191, 15442198064, 16190055003, 46870943027
Offset: 1

Views

Author

Giovanni Resta, Feb 06 2006

Keywords

Comments

a(26) > 5*10^10. 205447718981 is also a term. - Donovan Johnson, Sep 30 2011

Examples

			sigma(15463)*phi(15463) = 18056*12972 = 234222432.

Crossrefs

Cf. A084122, A115890, A115891.

Extensions

a(19)-a(25) from Donovan Johnson, Sep 30 2011

A115893 Numbers k such that sigma(k)*prime(k) is a palindrome.

Original entry on oeis.org

1, 2, 5, 4813, 47619
Offset: 1

Views

Author

Giovanni Resta, Feb 06 2006

Keywords

Comments

No additional terms up to 5*10^6. - Harvey P. Dale, Sep 14 2012

Examples

			sigma(47619)*prime(47619) = 82992*580477 = 48174947184.

Crossrefs

Cf. A084122, A115890, A115894.

Programs

  • Mathematica
    dspQ[n_]:=Module[{c=IntegerDigits[DivisorSigma[1,n]Prime[n]]},c == Reverse[c]]; Select[Range[50000],dspQ] (* Harvey P. Dale, Sep 14 2012 *)
Showing 1-5 of 5 results.

Started in 1964 by Neil J. A. Sloane | Maintained by The OEIS Foundation Inc.

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