A379032 Numbers k such that k and k+1 have an equal sum of modified exponential divisors: A241405(k) = A241405(k+1).

14, 44, 957, 1334, 1485, 1634, 1652, 2204, 2685, 3195, 3451, 3956, 4136, 5547, 8495, 8636, 8907, 9844, 11515, 12256, 14876, 15608, 19491, 20145, 20155, 27519, 27643, 33998, 35235, 36575, 38180, 41265, 41547, 42818, 45716, 48364, 74918, 79316, 79826, 79833, 84134

Offset: 1

Author

Amiram Eldar, Dec 14 2024

Keywords

• nonn

Links

• Amiram Eldar, Table of n, a(n) for n = 1..1918 (terms below 10^10)

Crossrefs

Cf. A241405.

Similar sequences: A002961, A064115, A064125, A293183, A306985.

Programs

Mathematica

f[p_, e_] := DivisorSum[e + 1, p^(# - 1) &]; mesigma[1] = 1; mesigma[n_] := mesigma[n] = Times @@ f @@@ FactorInteger[n]; Select[Range[10^5], mesigma[#] == mesigma[#+1] &]

PARI

mesigma(n) = {my(f=factor(n)); prod(i=1, #f~, sumdiv(f[i, 2]+1, d, f[i, 1]^(d-1))); }
lista(kmax) = {my(m1 = 1, m2); for(k = 2, kmax, m2 = mesigma(k); if(m1 == m2, print1(k-1, ", ")); m1 = m2);}