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 A276075 a(1) = 0, a(n) = (e1*i1! + e2*i2! + ... + ez*iz!) for n = prime(i1)^e1 * prime(i2)^e2 * ... * prime(iz)^ez, where prime(k) is the k-th prime, A000040(k). 15
 0, 1, 2, 2, 6, 3, 24, 3, 4, 7, 120, 4, 720, 25, 8, 4, 5040, 5, 40320, 8, 26, 121, 362880, 5, 12, 721, 6, 26, 3628800, 9, 39916800, 5, 122, 5041, 30, 6, 479001600, 40321, 722, 9, 6227020800, 27, 87178291200, 122, 10, 362881, 1307674368000, 6, 48, 13, 5042, 722, 20922789888000, 7, 126, 27, 40322, 3628801, 355687428096000, 10, 6402373705728000, 39916801, 28, 6, 726, 123 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,3 COMMENTS Additive with a(p^e) = e * (PrimePi(p)!), where PrimePi(n) = A000720(n). a(3181) has 1001 decimal digits. - Michael De Vlieger, Dec 24 2017 LINKS Michael De Vlieger, Table of n, a(n) for n = 1..3180 (First 120 terms from Antti Karttunen). FORMULA a(1) = 0; for n > 1, a(n) = a(A028234(n)) + (A067029(n) * A000142(A055396(n))). Other identities. For all n >= 0: a(A276076(n)) = n. a(A002110(n)) = A007489(n). a(A019565(n)) = A059590(n). a(A206296(n)) = A276080(n). a(A260443(n)) = A276081(n). For all n >= 1: a(A000040(n)) = n! = A000142(n). a(A076954(n-1)) = A033312(n). MATHEMATICA Array[If[# == 1, 0, Total[FactorInteger[#] /. {p_, e_} /; p > 1 :> e PrimePi[p]!]] &, 66] (* Michael De Vlieger, Dec 24 2017 *) PROG (Scheme, with memoization-macro definec) (definec (A276075 n) (cond ((= 1 n) (- n 1)) (else (+ (* (A067029 n) (A000142 (A055396 n))) (A276075 (A028234 n)))))) (Python) from sympy import factorint, factorial as f, primepi def a(n):     F=factorint(n)     return 0 if n==1 else sum(F[i]*f(primepi(i)) for i in F) print([a(n) for n in range(1, 121)]) # Indranil Ghosh, Jun 21 2017 CROSSREFS Cf. A000040, A000142, A000720, A002110, A007489, A019565, A028234, A033312, A055396, A059590, A067029, A076954, A206296, A260443, A276080, A276081. Left inverse of A276076. Cf. also A048675. Sequence in context: A266479 A296147 A130712 * A321908 A130728 A276085 Adjacent sequences:  A276072 A276073 A276074 * A276076 A276077 A276078 KEYWORD nonn AUTHOR Antti Karttunen, Aug 18 2016 STATUS approved

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Last modified July 29 09:31 EDT 2021. Contains 346344 sequences. (Running on oeis4.)