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A066077
a(n) is the number of x such that sigma(x)-1 is 0 or one of the first n-1 primes.
11
1, 2, 3, 4, 5, 7, 8, 10, 11, 14, 15, 17, 18, 21, 22, 25, 27, 30, 31, 32, 37, 38, 40, 43, 46, 48, 49, 51, 53, 54, 56, 58, 60, 61, 63, 64, 66, 67, 68, 74, 75, 79, 81, 86, 87, 88, 89, 90, 93, 96, 97, 100, 107, 108, 114, 115, 117, 120, 122, 123, 124, 125, 128, 130, 134, 135
OFFSET
1,2
COMMENTS
Former name was: Smallest x such that p(n) = Sigma[x] - 1. That did not match the Data. See A296375 for that sequence.
FORMULA
a(n+1)-a(n) = A066075(n).
MAPLE
N:= 100: # To get a(1)..a(N)
P:= ithprime(N-1):
S:= select(t -> isprime(t) and t <= P, map(-1+numtheory:-sigma, [$1..P])):
T:= Statistics:-Tally(sort(S), output=table):
ListTools:-PartialSums([1, seq(T[ithprime(i)], i=1..N-1)]); # Robert Israel, Dec 27 2017
PROG
(PARI) first(n) = my(res = vector(n), a = 1); res[1] = 1; for(k=2, n, for(x=1, prime(k-1), if(prime(k-1) == (sigma(x) - 1), a++)); res[k] = a); res \\ Iain Fox, Dec 28 2017
KEYWORD
nonn
AUTHOR
Labos Elemer, Dec 03 2001
EXTENSIONS
Edited by Robert Israel, Dec 27 2017
STATUS
approved