The OEIS mourns the passing of Jim Simons and is grateful to the Simons Foundation for its support of research in many branches of science, including the OEIS.
The OEIS is supported by the many generous donors to the OEIS Foundation.

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A247826 Numbers n with at least one nonpalindromic divisor such that the sum of sigma(x) = the sum of sigma(reverse(x)), where x runs over the divisors of n. 1
 16331, 98639, 161051, 179641, 272802, 1206611, 1226221, 1649431, 1794971, 6061206, 6177253, 8792914 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 LINKS Table of n, a(n) for n=1..12. EXAMPLE Divisors of 16331 are 1, 7, 2333, 16331; sigma(1) = 1, sigma(7) = 8, sigma(2333) = 2334, sigma(16331) = 18672 and 1 + 8 + 2334 + 18672 = 21015. sigma(1) = 1, sigma(7) = 8, sigma(3332) = 7182, sigma(13361) = 13824 and 1 + 8 + 7182 + 13824 = 21015. Divisors of 98639 are 1, 98639; sigma(1) = 1, sigma(98639) = 98640, and 1 + 98640 = 98641. sigma(1) = 1, sigma(93689) = 98640, and 1 + 98640 = 98641. MAPLE with(numtheory); T:=proc(h) local x, y, w; x:=h; y:=0; for w from 1 to ilog10(h)+1 do y:=10*y+(x mod 10); x:=trunc(x/10); od; y; end: P:=proc(q) local a, b, c, k, n, ok; for n from 1 to q do a:=divisors(n); b:=0; c:=0; ok:=0; for k from 1 to nops(a) do b:=b+sigma(T(a[k])); c:=c+sigma(a[k]); if a[k]<>T(a[k]) then ok:=1; fi; od; if ok=1 and c=b then print(n); fi; od; end: P(10^9); PROG (PARI) rev(n) = subst(Polrev(digits(n)), x, 10); isok(n) = {nbpal = sumdiv(n, d, rev(d)==d); if (nbpal == numdiv(n), return(0)); sumdiv(n, d, sigma(d)) == sumdiv(n, d, sigma(rev(d))); } \\ Michel Marcus, Oct 04 2014 (PARI) rev(n)=r=""; d=digits(n); for(i=1, #d, r=concat(Str(d[i]), r)); eval(r) for(n=1, 10^6, D=divisors(n); c=0; for(k=1, #D, if(D[k]==rev(D[k]), c++)); if(c!=#D, if(sumdiv(n, i, sigma(i))==sumdiv(n, j, sigma(rev(j))), print1(n, ", ")))) \\ Derek Orr, Oct 26 2014 CROSSREFS Cf. A000203, A196677, A246545. Sequence in context: A058552 A337417 A013690 * A223109 A126824 A236778 Adjacent sequences: A247823 A247824 A247825 * A247827 A247828 A247829 KEYWORD nonn,more,base,hard AUTHOR Paolo P. Lava, Sep 30 2014 EXTENSIONS a(6)-a(12) from Michel Marcus, Oct 04 2014 Definition edited by Derek Orr, Oct 26 2014 STATUS approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recents
The OEIS Community | Maintained by The OEIS Foundation Inc.

Last modified June 17 23:07 EDT 2024. Contains 373467 sequences. (Running on oeis4.)