OFFSET
1,2
COMMENTS
The modified exponential divisors of a number n = product p_i^r_i are all numbers of the form product p_i^s_i such that s_i+1 divides r_i+1 for each i.
Number of modified exponential divisors coincides with number of exponential divisors A049419.
LINKS
Antti Karttunen, Table of n, a(n) for n = 1..16384
David Moews, Perfect, amicable and sociable numbers.
FORMULA
MATHEMATICA
f[p_, e_] := DivisorSum[e+1, p^(#-1)&]; a[1] = 1; a[n_] := Times @@ f @@@ FactorInteger[n]; Array[a, 100] (* Amiram Eldar, Sep 03 2023 *)
PROG
(PARI) A241405(n) = {my(f=factor(n)); prod(i=1, #f[, 1], sumdiv(f[i, 2]+1, d, f[i, 1]^(d-1)))}
CROSSREFS
KEYWORD
nonn,easy,mult
AUTHOR
Andrew Lelechenko, May 06 2014
EXTENSIONS
More terms from Antti Karttunen, Nov 23 2017
STATUS
approved