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%I #27 Mar 03 2023 06:34:10
%S 3,4,6,7,9,13,14,18,21,25,26,28,31,33,36,42,43,44,49,50,62,66,73,86,
%T 87,91,95,98,111,116,117,121,135,146,148,152,157,161,169,174,182,190,
%U 201,207,211,216,222,228,234,237,241,242,252,268,270,287,289,305
%N Numbers m such that phi(m) is an oblong number.
%C An oblong number (A002378) is of the form k*(k+1) where k is a natural number.
%C From _Bernard Schott_, Feb 27 2023: (Start)
%C Subsequence of primes is A002383 because in this case phi(k^2+k+1) = k*(k+1).
%C Subsequence of oblong numbers is A359847 where k and phi(k) are both oblong numbers. (End)
%H Giovanni Resta, <a href="/A236386/b236386.txt">Table of n, a(n) for n = 1..10000</a>
%e phi(13) = 12 = 3*4, an oblong number; so 13 is a term of the sequence.
%p filter := m -> issqr(1 + 4*phi(m)) : select(filter, [$(1 .. 700)]); # _Bernard Schott_, Feb 26 2023
%t Select[Range[500], IntegerQ@Sqrt[1 + 4*EulerPhi[#]] &] (* _Giovanni Resta_, Jan 24 2014 *)
%o (PARI) isok(m) = my(t=eulerphi(m)); !(t%2) && ispolygonal(t/2, 3); \\ _Michel Marcus_, Feb 27 2023
%o (Python)
%o from itertools import count, islice
%o from sympy.ntheory.primetest import is_square
%o from sympy import totient
%o def A236386_gen(startvalue=1): # generator of terms >= startvalue
%o return filter(lambda n:is_square((totient(n)<<2)+1), count(max(1,startvalue)))
%o A236386_list = list(islice(A236386_gen(),20)) # _Chai Wah Wu_, Feb 28 2023
%Y Cf. A000010, A002378, A002383, A359847.
%Y Similar, but where phi(m) is: A039770 (square), A039771 (cube), A078164 (biquadrate), A096503 (repdigit), A117296 (palindrome), A360944 (triangular).
%K nonn,easy
%O 1,1
%A _Joseph L. Pe_, Jan 24 2014
%E a(16)-a(58) from _Giovanni Resta_, Jan 24 2014
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