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.
login
The OEIS is supported by the many generous donors to the OEIS Foundation.

 

Logo
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
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
Sequence in context: A058552 A337417 A013690 * A223109 A126824 A236778
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.

License Agreements, Terms of Use, Privacy Policy. .

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