A323759 Larger of modified exponential amicable pairs.

126, 378, 1260, 3780, 4584, 5544, 11424, 16632, 16728, 49308, 68760, 73962, 88608, 179118, 168730, 212160, 225096, 256338, 266568, 250920, 365700, 374304, 391656, 374418, 387720, 386568, 393528, 548550, 827700, 739620, 827652, 932100, 912288, 935400, 1052088

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 lesser counterparts are in A323758.

Links

• Amiram Eldar, Table of n, a(n) for n = 1..4725 (terms whose lesser counterparts below 2*10^11)
• David Moews, Perfect, amicable and sociable numbers.

Crossrefs

Cf. A241405, A323757, A323758.

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, m]], {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 > 0) && (fn < n) && (fm(fn) == n); \\ Michel Marcus, Jan 30 2019