A339982 Coreful abundant numbers (A308053) with an odd sum of coreful divisors.

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

Amiram Eldar, Table of n, a(n) for n = 1..1000

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.

Cf. A007947, A057723, A339979.

Sequence in context: A234979 A233874 A084554 * A234554 A192104 A210181

Adjacent sequences: A339979 A339980 A339981 * A339983 A339984 A339985

Keyword

nonn

Author

Amiram Eldar, Dec 25 2020

Status

approved