Year-end appeal: Please make a donation to the OEIS Foundation to support ongoing development and maintenance of the OEIS. We are now in our 61st year, we have over 378,000 sequences, and we’ve reached 11,000 citations (which often say “discovered thanks to the OEIS”).
%I #15 Jun 09 2024 08:50:51
%S 3,4,4,6,8,5,5,12,14,6,18,20,24,7,6,30,32,7,38,42,44,48,9,54,60,62,8,
%T 68,72,74,80,7,84,90,98,102,104,108,110,114,13,8,128,9,132,138,140,
%U 150,152,158,164,168,15,174,180,182,192,194,198,200,212,224,228,230,234,240,242
%N Sum of base and exponent of prime powers.
%C If n = p^q, where p is prime and q > 0, then p+q is in the sequence.
%C If n is not of that form, omit the term.
%C Might be a good "puzzle" sequence - guess the rule given the first ten or so terms.
%H Michael De Vlieger, <a href="/A112376/b112376.txt">Table of n, a(n) for n = 1..10000</a>
%e n = 3 = 3^1, so 3+1 = 4 is a term; n = 4 = 2^2, so 2+2 = 4 is again a term; n = 5 = 5^1, so we get 5+1 =6.
%e But 6 is not a prime power, so we skip it.
%t fsum[a_] := Total[Flatten[FactorInteger[a]]]; fsum/@Select[Range[242], PrimePowerQ](* _James C. McMahon_, Jun 08 2024 *)
%o (PARI) for(n=1,300,fac=factor(n);if(matsize(fac)[1]==1,print1(fac[1,1]+fac[1,2],",")))
%Y Cf. A112375, A064438.
%Y A008474 is another version, defined for all n.
%K nonn
%O 1,1
%A _Zak Seidov_, Dec 04 2005
%E Edited and extended by _Klaus Brockhaus_, Jan 21 2006
%E Further edited by _N. J. A. Sloane_, Nov 19 2018