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A036288 a(n) = 1 + integer log of n: if the prime factorization of n is n = Product (p_j^k_j) then a(n) = 1 + Sum (p_j * k_j) (cf. A001414). 6

%I

%S 1,3,4,5,6,6,8,7,7,8,12,8,14,10,9,9,18,9,20,10,11,14,24,10,11,16,10,

%T 12,30,11,32,11,15,20,13,11,38,22,17,12,42,13,44,16,12,26,48,12,15,13,

%U 21,18,54,12,17,14,23,32,60,13,62,34,14,13,19,17,68,22

%N a(n) = 1 + integer log of n: if the prime factorization of n is n = Product (p_j^k_j) then a(n) = 1 + Sum (p_j * k_j) (cf. A001414).

%C If this function is iterated then, starting at any number n >= 7, we will always reach an 8 - see A212813, A212814, A212815. - From _N. J. A. Sloane_, May 30 2012

%C a(n) = sum (A027748(k) * A124010(k): k = 1 .. A001221(n)) + 1. - _Reinhard Zumkeller_, May 30 2012

%D Bellamy, O. S.; Cadogan, C. C. Subsets of positive integers: their cardinality and maximality properties. Proceedings of the Tenth Southeastern Conference on Combinatorics, Graph Theory and Computing (Florida Atlantic Univ., Boca Raton, Fla., 1979), pp. 167--178, Congress. Numer., XXIII-XXIV, Utilitas Math., Winnipeg, Man., 1979. MR0561043 (82b:10006) - From _N. J. A. Sloane_, May 30 2012

%D R. Honsberger, Problem 89, Another Curious Sequence, Mathematical Morsels, MAA, 1978, pp. 223-227.

%H Reinhard Zumkeller, <a href="/A036288/b036288.txt">Table of n, a(n) for n = 1..10000</a>

%H J. B. Roberts, <a href="http://www.jstor.org/stable/2317575">Problem E2356</a>, Amer. Math. Monthly, 79 (1972); <a href="http://www.jstor.org/stable/2318177">solution</a> by H. Kappus, loc. cit., 80 (1973), p. 810.

%e 12=2^2*3 so a(12)=1+2^2+3=8.

%p f:=proc(n) local i,t1; t1:=ifactors(n)[2]; 1+add( t1[i][1]*t1[i][2], i=1..nops(t1)); end; # _N. J. A. Sloane_, May 30 2012

%t f[1]=1;f[n_]:=Total[Apply[Times,FactorInteger[n],1]]+1;f/@Range@68 (* _Ivan N. Ianakiev_, Apr 18 2016 *)

%o (Haskell)

%o a036288 n = 1 + sum (zipWith (*)

%o (a027748_row n) (map fromIntegral $ a124010_row n))

%o -- _Reinhard Zumkeller_, May 30 2012

%o (PARI) A036288(n)=1+(n=factor(n))[,1]~*n[,2] \\ _M. F. Hasler_, May 30 2012

%Y Equals A001414 + 1.

%Y Cf. A212813, A212814, A212815, A212816, A212908, A212909.

%K nonn

%O 1,2

%A _N. J. A. Sloane_

%E Edited by _N. J. A. Sloane_, Jun 01 2012

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Last modified October 21 16:20 EDT 2019. Contains 328302 sequences. (Running on oeis4.)