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A339982
Coreful abundant numbers (A308053) with an odd sum of coreful divisors.
2
1157625, 10418625, 12733875, 15049125, 19679625, 21994875, 26625375, 28940625, 33571125, 35886375, 40429125, 42832125, 47462625, 49777875, 54408375, 56723625, 61354125, 66733875, 68299875, 70615125, 77560875, 82191375, 84506625, 91452375, 93767625, 96082875
OFFSET
1,1
COMMENTS
A coreful divisor d of a number k is a divisor with the same set of distinct prime factors as k, or rad(d) = rad(k), where rad(k) is the largest squarefree divisor of k (A007947).
All the terms are odd numbers since the sum of coreful divisors (A057723) of an even number is even.
All the terms are exponentially odd numbers (A268335) since the sum of coreful divisors function is multiplicative and A057723(p^e) = p + p^2 + ... + p^e is even for a prime p and an even exponent e.
None of the terms are coreful Zumkeller numbers (A339979).
LINKS
EXAMPLE
1157625 is a term since A057723(1157625) = 2411955 > 2*1157625 and it is odd.
MATHEMATICA
f[p_, e_] := (p^(e + 1) - 1)/(p - 1) - 1; s[1] = 1; s[n_] := Times @@ (f @@@ FactorInteger[n]); Select[Range[1, 2*10^7, 2], (sum = s[#]) > 2*# && OddQ[sum] &]
CROSSREFS
Intersection of A268335 and A339936.
Subsequence of A308053.
Sequence in context: A234979 A233874 A084554 * A234554 A192104 A210181
KEYWORD
nonn
AUTHOR
Amiram Eldar, Dec 25 2020
STATUS
approved