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

Author

Amiram Eldar, Dec 25 2020

Keywords

• nonn

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).

Examples

			1157625 is a term since A057723(1157625) = 2411955 > 2*1157625 and it is odd.
		

Links

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

Crossrefs

Intersection of A268335 and A339936.

Subsequence of A308053.

Cf. A007947, A057723, A339979.

Programs

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] &]