

A257973


Palindromes with no palindromic aliquot parts except 1.


1



323, 767, 949, 989, 10001, 11111, 11611, 11911, 12121, 12521, 13031, 13631, 14041, 14141, 14941, 15151, 15751, 16861, 17071, 17371, 17671, 17771, 18581, 18881, 19091, 31813, 32023, 32723, 33133, 33233, 33433, 33833, 34043, 34343, 34943, 35953, 36163, 36763, 37973
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OFFSET

1,1


COMMENTS

The definition implies that the prime factors are not palindromes. The converse is not true. For instance, prime factors of 1681861 are 17, 19, 41, 127, which are not palindromes, but its aliquot parts are 1, 17, 19, 41, 127, 323, 697, 779, 2159, 2413, 5207, 13243, 41021, 88519, 98933, and 323 is a palindrome.
Mainly squarefree numbers. Not squarefree are 36163 = 29^2*43, 39593 = 17^2*137, 71117 = 19^2*197, 94249 = 307^2, 95659 = 17^2*331, 1069601 = 13^2*6329, etc.
There are large jumps: from a(4) = 989 to a(5) = 10001; from a(97) = 99499 to a(98) = 1005001; from a(380) = 1996991 to a(381) = 3004003; from a(677) = 3995993 to a(678) = 7002007; from a(985) = 7999997 to a(986) = 9001009; etc.
The first two squares in the sequence are 94249 = 307^2 and 1230127210321 = 509^2 * 2179^2.  Giovanni Resta, May 15 2015


LINKS

Paolo P. Lava, Table of n, a(n) for n = 1..1000


EXAMPLE

Aliquot parts of 323 are 1, 17, 19 that are not palindromes, except 1.
Aliquot parts of 767 are 1, 13, 59 that are not palindromes, except 1.
Aliquot parts of 12121 are 1, 17, 23, 31, 391, 527, 713 that are not palindromes, except 1.


MAPLE

with(numtheory): T:=proc(w) local x, y, z; x:=w; y:=0;
for z from 1 to ilog10(x)+1 do y:=10*y+(x mod 10);
x:=trunc(x/10); od; y; end:
P:=proc(q) local a, j, k, ok, n;
for n from 2 to q do if n=T(n) then a:=ifactors(n)[2]; ok:=1;
for k from 1 to nops(a) do if a[k][1]=T(a[k][1]) then ok:=0; break; fi;
od; if ok=1 then print(n); fi; fi; od; end: P(10^9);


CROSSREFS

Cf. A002113.
Sequence in context: A065822 A279072 A158306 * A083138 A121209 A065884
Adjacent sequences: A257970 A257971 A257972 * A257974 A257975 A257976


KEYWORD

nonn,easy,base


AUTHOR

Paolo P. Lava, May 15 2015


STATUS

approved



