

A241405


Sum of modified exponential divisors: if n = product p_i^r_i then mesigma(x) = product (sum p_i^s_i such that s_i+1 divides r_i+1).


6



1, 3, 4, 5, 6, 12, 8, 11, 10, 18, 12, 20, 14, 24, 24, 17, 18, 30, 20, 30, 32, 36, 24, 44, 26, 42, 31, 40, 30, 72, 32, 39, 48, 54, 48, 50, 38, 60, 56, 66, 42, 96, 44, 60, 60, 72, 48, 68, 50, 78, 72, 70, 54, 93, 72, 88, 80, 90, 60, 120, 62, 96, 80, 65, 84, 144, 68, 90, 96, 144, 72, 110, 74, 114, 104, 100, 96, 168, 80
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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.
The concept of modified exponential divisors simplifies combinatorial problems on the sum of exponential divisors A051377 such as a search of eperfect numbers. Each primitive eperfect number A054980 corresponds to a unique meperfect number of smaller magnitude.


LINKS

Antti Karttunen, Table of n, a(n) for n = 1..16384
D. Moews, Perfect, amicable and sociable numbers
Index entries for sequences related to sums of divisors


FORMULA

a(n / A007947(n)) = A051377(n).
Multiplicative with a(p^a) = sum p^b such that b+1 divides a+1.


PROG

(PARI) A241405(n) = {my(f=factor(n)); prod(i=1, #f[, 1], sumdiv(f[i, 2]+1, d, f[i, 1]^(d1)))}


CROSSREFS

Cf. A049419, A051377, A054980, A051378.
Sequence in context: A034448 A069184 A181549 * A322485 A324706 A049417
Adjacent sequences: A241402 A241403 A241404 * A241406 A241407 A241408


KEYWORD

nonn,mult


AUTHOR

Andrew Lelechenko, May 06 2014


EXTENSIONS

More terms from Antti Karttunen, Nov 23 2017


STATUS

approved



