A323758 Lesser of modified exponential amicable pairs.

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

Author

Amiram Eldar, Jan 26 2019

Keywords

• nonn

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)
• David Moews, Perfect, amicable and sociable numbers.

Crossrefs

Cf. A241405, A323757, A323759.

Programs

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

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