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 A331602 a(1) = 0; for n > 1, a(n) = A007947(A156552(n)). 1
 0, 1, 2, 3, 2, 5, 2, 7, 6, 3, 2, 11, 2, 17, 10, 15, 2, 13, 2, 19, 6, 33, 2, 23, 6, 65, 14, 35, 2, 21, 2, 31, 34, 129, 10, 3, 2, 257, 66, 39, 2, 37, 2, 67, 22, 57, 2, 47, 6, 5, 130, 131, 2, 29, 6, 71, 258, 205, 2, 43, 2, 2049, 38, 21, 34, 69, 2, 259, 514, 41, 2, 55, 2, 4097, 26, 515, 10, 133, 2, 79, 30, 8193, 2, 15, 66, 16385, 114, 15, 2, 15, 6, 1027, 410, 10923 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,3 LINKS Antti Karttunen, Table of n, a(n) for n = 1..10000 (based on Hans Havermann's factorization of A156552) FORMULA a(1) = 0; and for n > 1, a(n) = A007947(A156552(n)). A000035(a(n)) = 1 - A000035(n). [Flips the parity] MATHEMATICA Array[Times @@ FactorInteger[#][[All, 1]] &@ Floor@ Total@ Flatten@ MapIndexed[#1 2^(#2 - 1) &, Flatten[Table[2^(PrimePi@ #1 - 1), {#2}] & @@@ FactorInteger@ #]] &, 94] (* Michael De Vlieger, Jan 24 2020 *) PROG (PARI) A007947(n) = factorback(factorint(n)[, 1]); A156552(n) = {my(f = factor(n), p2 = 1, res = 0); for(i = 1, #f~, p = 1 << (primepi(f[i, 1]) - 1); res += (p * p2 * (2^(f[i, 2]) - 1)); p2 <<= f[i, 2]); res}; \\ From A156552 A331602(n) = A007947(A156552(n)); CROSSREFS Cf. A000035, A007947, A156552. Cf. also A322993. Sequence in context: A096776 A280687 A271774 * A118176 A005731 A132962 Adjacent sequences:  A331599 A331600 A331601 * A331603 A331604 A331605 KEYWORD nonn AUTHOR Antti Karttunen, Jan 22 2020 STATUS approved

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Last modified July 28 19:33 EDT 2021. Contains 346335 sequences. (Running on oeis4.)