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 A322079 a(n) = n^2 * Sum_{ p^k | n } k / p^2, where p are primes dividing n with multiplicity k. 0
 0, 1, 1, 8, 1, 13, 1, 48, 18, 29, 1, 88, 1, 53, 34, 256, 1, 153, 1, 216, 58, 125, 1, 496, 50, 173, 243, 408, 1, 361, 1, 1280, 130, 293, 74, 936, 1, 365, 178, 1264, 1, 673, 1, 984, 531, 533, 1, 2560, 98, 825, 298, 1368, 1, 1701, 146, 2416, 370, 845, 1, 2344, 1 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,4 COMMENTS Generalized formula is f(n,m) = n^m * Sum_{p^k|n} k/p^m, where f(n,0) = A001222(n) and f(n,1) = A003415(n). LINKS EXAMPLE a(40) = 1264 because 40 = 2^3 * 5, so we have 40^2 * (3/2^2 + 1/5^2) = 1264. MATHEMATICA f[p_, e_] := e/p^2; a[n_] := If[n==1, 0, n^2*Plus@@f@@@FactorInteger[n]]; Array[a, 60] (* Amiram Eldar, Nov 26 2018 *) PROG (PARI) a(n) = my(f=factor(n)); sum(k=1, #f~, (n^2\f[k, 1]^2)*f[k, 2]); CROSSREFS Cf. A001222, A003415. Sequence in context: A045771 A070488 A349142 * A124906 A298143 A181762 Adjacent sequences:  A322076 A322077 A322078 * A322080 A322081 A322082 KEYWORD nonn AUTHOR Daniel Suteu, Nov 25 2018 STATUS approved

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Last modified November 29 04:38 EST 2021. Contains 349416 sequences. (Running on oeis4.)