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A374330
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a(n) is the number of numbers k <= prime(n)^2 such that A075860(k) = prime(n).
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0
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2, 2, 6, 8, 2, 10, 3, 14, 6, 8, 22, 7, 8, 21, 9, 14, 12, 45, 14, 17, 45, 17, 21, 20, 18, 17, 64, 21, 54, 28, 25, 22, 22, 72, 37, 82, 26, 28, 31, 43, 36, 93, 44, 95, 38, 95, 41, 38, 33, 106, 36, 49, 111, 65, 53, 53, 49, 113, 55, 68, 138, 80, 49, 50, 152, 61, 55, 43, 73, 120
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OFFSET
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1,1
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COMMENTS
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For all n>=1, a(n)>=2.
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LINKS
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EXAMPLE
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For n=3, prime(3)=5. The only integers k <= 5^2 such that A075860(k)=5 are 5,6,12,18,24 and 25. Therefore a(3)=6.
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MAPLE
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f := proc (n)
option remember;
if isprime(n) then
return n
else
return procname(convert(numtheory:-factorset(n), `+`))
end if
end proc:
g := proc (n)
local count, k;
count := 0;
for k from ithprime(n) to ithprime(n)^2 do
if f(k) = ithprime(n) then
count := count + 1
end if
end do;
return count
end proc:
map(g, [$1 .. 80]);
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PROG
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(PARI) fp(n, pn) = if (n == pn, n, fp(vecsum(factor(n)[, 1]), n));
f(n) = if (n==1, 0, fp(n, 0)); \\ A075860
a(n) = sum(k=1, prime(n)^2, f(k) == prime(n)); \\ Michel Marcus, Jul 04 2024
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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