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.

16331, 98639, 161051, 179641, 272802, 1206611, 1226221, 1649431, 1794971, 6061206, 6177253, 8792914

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