A238922 Numbers n such that Sum_{i=1..j} 1/d(i) - Sum_{i=1..k} 1/p(i) is an integer, where p are the prime factors of n, counted with multiplicity, and d its divisors.

1, 12, 18, 220, 396, 17296, 24016, 287532, 4661056, 64288512, 334144656, 358585488, 555192576, 568719616, 2172649216, 2451538112, 2645953344, 2955423888, 6704333824, 26996772032, 88734733632, 147861504000, 311063879024, 371226582848, 429391876096

Offset

1,2

Comments

A212128 and A230164 are subsets of this sequence.

a(26) > 10^12. - Giovanni Resta, Mar 11 2014

Links

Table of n, a(n) for n=1..25.

Example

Divisors of 12 are 1, 2, 3, 4, 6, 12 and 1/1 + 1/2 + 1/3 +1/4 + 1/6 + 1/12 = 7/3. Prime factors of 12 are 2^2, 3 and 1/2 + 1/2 + 1/3 = 4/3. Finally 7/3 - 4/3 = 1 that is an integer.

Maple

with(numtheory); P:=proc(q) local a, b, c, k, n;
for n from 1 to q do if not isprime(n) then b:=sigma(n)/n;
a:=ifactors(n)[2]; c:=add(a[k][2]/a[k][1], k=1..nops(a));
if type(b-c, integer) then lprint(n, b-c); fi; fi; od; end: P(10^6);

Crossrefs

Cf. A003415, A212128, A224346, A230164.

Sequence in context: A258427 A166627 A018957 * A212128 A110932 A112880

Adjacent sequences: A238919 A238920 A238921 * A238923 A238924 A238925

Keyword

nonn,hard

Author

Paolo P. Lava, Mar 07 2014

Extensions

a(9)-a(10), a(13)-a(17), a(19)-a(25) from Giovanni Resta, Mar 11 2014

Status

approved