|
|
A072627
|
|
Number of divisors d of n such that d-1 is prime.
|
|
14
|
|
|
0, 0, 1, 1, 0, 2, 0, 2, 1, 0, 0, 4, 0, 1, 1, 2, 0, 3, 0, 2, 1, 0, 0, 6, 0, 0, 1, 2, 0, 3, 0, 3, 1, 0, 0, 5, 0, 1, 1, 3, 0, 4, 0, 2, 1, 0, 0, 7, 0, 0, 1, 1, 0, 4, 0, 3, 1, 0, 0, 7, 0, 1, 1, 3, 0, 2, 0, 2, 1, 1, 0, 8, 0, 1, 1, 2, 0, 2, 0, 4, 1, 0, 0, 7, 0, 0, 1, 3, 0, 5, 0, 1, 1, 0, 0, 8, 0, 2, 1, 2, 0, 3, 0, 3, 1
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
OFFSET
|
1,6
|
|
COMMENTS
|
If n == 3 (mod 6) then a(n)=1; a(n) = 0 for all other odd n. - Robert Israel, Dec 27 2018
|
|
LINKS
|
|
|
FORMULA
|
If p is prime <> 3, then divisors(p)-1 = {1,p}-1 = {0,p-1}, so a(p) = 0.
|
|
EXAMPLE
|
n=240: a(240)=12 because primes of -1+d form are: {2,3,5,7,11,19,23,29,47,59,79,239}. These and only these divisors are present in any InvSigma of n, like:InvSig[240]= {114,135,158,177,203,209,239} with {2,3,19,3,5,2,79,3,59,7,29,11,19,239} p-divisors.
|
|
MAPLE
|
f:= n -> nops(select(t -> isprime(t-1), numtheory:-divisors(n))):
|
|
MATHEMATICA
|
di[x_] := Divisors[x] dp[x_] := Part[di[x], Flatten[Position[PrimeQ[ -1+di[x]], True]]]-1 Table[Length[dp[w]], {w, 1, 128}]
Table[Count[Divisors[n], _?(PrimeQ[#-1]&)], {n, 110}] (* Harvey P. Dale, Jul 04 2021 *)
|
|
PROG
|
(Haskell)
a072627 = length . filter ((== 1) . a010051 . (subtract 1)) . a027749_row
(PARI) a(n) = sumdiv(n, d, isprime(d-1)); \\ Michel Marcus, Dec 27 2018
|
|
CROSSREFS
|
|
|
KEYWORD
|
nonn
|
|
AUTHOR
|
|
|
STATUS
|
approved
|
|
|
|