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A238922 Numbers n such that Sum_{i=1..j} 1/d(i) - Sum_{i=1..k} 1/p(i) is integer, where p are the prime factors of n, counted with multiplicity, and d its divisors. 0
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 (list; graph; refs; listen; history; text; internal format)
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 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

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Last modified October 19 23:51 EDT 2021. Contains 348095 sequences. (Running on oeis4.)