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A318988
Totients whose inverses contain two or more consecutive tetrahedral pyramidal numbers.
0
24, 80, 256, 880, 3840, 8096, 96768, 380160, 552960, 2336256, 6209280, 7600320, 7741440, 10579968, 25090560, 32845824, 34031616, 34594560, 35610624
OFFSET
1,1
COMMENTS
For a(1) = A000010(A000292(5)) = A000010(A000292(6)) = A000010(A000292(7)), this reduces to A000010(5*7) = A000010(8*7) = A000010(12*7). The number 7 is relatively prime to 5, 8, and 12 which are inverses of the totient value 4. 7 appears in the numerator of A000292(5), A000292(6), and A000292(7). Following the same process 11 and 17 replace 7 for a(2) and a(3).
Conjecture: There are at most three consecutive tetrahedral pyramidal numbers in the set of inverses of a totient number.
EXAMPLE
24 is a term because A000010(A000292(5)) = A000010(A000292(6)) = A000010(A000292(7)) = 24.
80 is a term because A000010(A000292(9)) = A000010(A000292(10)) = 80.
380160 is a term because A000010(A000292(182)) = A000010(A000292(183)) = A000010(A000292(184)) = 380160.
CROSSREFS
Sequence in context: A211583 A211589 A211597 * A182915 A030622 A063456
KEYWORD
nonn
AUTHOR
Torlach Rush, Sep 06 2018
STATUS
approved