A136025 Sum of distinct proper prime divisors of odd integers below 10^n.

3, 373, 24307, 1691682, 127867801, 10233538789, 850896280551, 72812857079241, 6363727756215813, 565232434009370012, 50843507342073211151, 4620323131256374760046, 423405369424475640435621, 39074878176445767411791424

Offset: 1

Author

Enoch Haga, Dec 12 2007

Keywords

• more
• nonn

Comments

Through 10^5 about 37.5% of total sums for all integers N comprise sums of odd N and the remaining 62.5% of even N.

Examples

			a(0)=3 because the only odd N <=10^1-1 having a prime factor is 9 and its factor is 3 and sum is 3.
		

Crossrefs

Cf. A136021, A136024, A143851.

Programs

Maple

A105221 := proc(n) local a,ifs,p; ifs := ifactors(n)[2] ; a := 0 ; for p in ifs do if op(1,p) <> 1 and op(1,p) <> n then a := a+op(1,p) ; fi ; od: RETURN(a) ; end: A136025 := proc(n) local a,k ; a := 0 ; for k from 5 to 10^n-1 by 2 do a := a+A105221(k) ; od: RETURN(a) ; end: for n from 1 do print(A136025(n)); od: # R. J. Mathar, Jan 29 2008

Formula

a(n) = sum_{k=1,2,...,A093143(n)} A105221(2k-1). - R. J. Mathar, Jan 29 2008

a(n) = sum_{prime p, 3<=p<10^n} p*floor((10^n-p)/(2p)). - Max Alekseyev, Jan 30 2012

Extensions

a(6) from R. J. Mathar, Jan 29 2008

a(7)-a(11) from Max Alekseyev, Jan 30 2012

a(12)-a(14) from Hiroaki Yamanouchi, Jul 06 2014