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A231722
Partial sums of A001088 starting from its second term; a(1)=0, a(n) = A001088(2)+...+A001088(n).
5
0, 1, 3, 7, 23, 55, 247, 1015, 5623, 24055, 208375, 945655, 9793015, 62877175, 487550455, 3884936695, 58243116535, 384392195575, 6255075618295, 53220543000055, 616806151581175, 6252662237392375, 130241496125238775, 1122152167228009975, 20960365589283433975
OFFSET
1,3
COMMENTS
a(n+1) gives the index to the last term in each row of A231716. Specifically, for all n>=1, A231716(a(n+1)) = A033312(n+1).
a(n) = natural number which is written as the n-th repunit in "totient phi number system": 0, 1, 10, 11, 100, 101, 110, 111, 200, 201, 210, 211, 300, 301, 310, 311, 1000, 1001, 1010, 1011, 1100, 1101, 1110, 1111, 1200, ..., and so on. Note how the 1st, the 3rd, the 7th and 23rd terms of this list are 1, 11, 111, and 1111.
In this number system the i-th digit from right (the least significant digit = digit_0) may contain integers in range 0..A000010(i+3)-1, and the value of the number is obtained as sum_{i=0..} digit_i * A001088(i+2).
LINKS
FORMULA
a(n) = A231721(n)-1. [The terms are one less than the partial sums of "phitorials", A001088, cumulatively summed from their first term]
MAPLE
with(numtheory): A231722:=n->add(product(phi(k), k=1..i), i=2..n): seq(A231722(n), n=1..20); # Wesley Ivan Hurt, Aug 09 2014
MATHEMATICA
Table[Sum[Product[EulerPhi[k], {k, i}], {i, 2, n}], {n, 20}] (* Wesley Ivan Hurt, Aug 09 2014 *)
PROG
(Scheme)
(define (A231722 n) (- (A231721 n) 1))
(PARI) a(n) = sum(i=2, n, prod(k=1, i, eulerphi(k))); \\ Michel Marcus, Aug 09 2014
CROSSREFS
One less than A231721.
Cf. A000010 (Euler's totient function phi), A001088 (its partial products, "phitorials"), A231716, A033312.
Sequence in context: A179491 A219167 A293466 * A168612 A332866 A127178
KEYWORD
nonn
AUTHOR
Antti Karttunen, Nov 27 2013
STATUS
approved