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A323758
Lesser of modified exponential amicable pairs.
2
114, 366, 1140, 3660, 3864, 5016, 11040, 16104, 16536, 44772, 57960, 67158, 68640, 142290, 142310, 180960, 196248, 198990, 240312, 248040, 308220, 322080, 326424, 339822, 348840, 352632, 366792, 462330, 669900, 671580, 785148, 815100, 817440, 849240, 912072
OFFSET
1,1
COMMENTS
A modified exponential amicable pair (m, n) has A241405(m) = A241405(n) = m + n + 1.
The larger counterparts are in A323759.
LINKS
Amiram Eldar, Table of n, a(n) for n = 1..4725 (terms below 2*10^11)
MATHEMATICA
f[p_, e_] := DivisorSum[e+1, p^(#-1)&]; mesigma[1]=1; mesigma[n_] := Times @@ f @@@FactorInteger@ n; s={}; mes[n_] := mesigma[n]-n; Do[m=mes[n]; If[m>n && mes[m]==n, AppendTo[s, n]], {n, 1, 10000}]; s
PROG
(PARI) f(n) = {my(f=factor(n)); prod(i=1, #f[, 1], sumdiv(f[i, 2]+1, d, f[i, 1]^(d-1))); } \\ A241405
fm(n) = f(n) - n;
isok(n) = my(fn=fm(n)); (fn > n) && (fm(fn) == n); \\ Michel Marcus, Jan 30 2019
CROSSREFS
KEYWORD
nonn
AUTHOR
Amiram Eldar, Jan 26 2019
STATUS
approved