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

1,1

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)

David Moews, Perfect, amicable and sociable numbers.

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

Cf. A241405, A323757, A323759.

Sequence in context: A300478 A305066 A322541 * A043403 A122279 A251481

Adjacent sequences: A323755 A323756 A323757 * A323759 A323760 A323761

Keyword

nonn

Author

Amiram Eldar, Jan 26 2019

Status

approved