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 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 (list; graph; refs; listen; history; text; internal format)
 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

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Last modified May 7 02:20 EDT 2021. Contains 343636 sequences. (Running on oeis4.)