A120322 RF(11): refactorable numbers with 11 as smallest prime factor.

25937424601, 3575694237941010577249, 52289689788971837545849, 159024068785448665562401, 604292326212030787555081, 1074497011086501939579049, 10912062142819279835644801

Offset: 1

Author

Walter Kehowski, Jun 21 2006

Keywords

• nonn

Comments

See A033950 for references. For any prime p, p^(p-1) is the smallest element of RF(p), the refactorable numbers whose smallest prime factor is p. Thus 11^(11-1)=25937424601 is the first element. Other elements would also be 11^10*17^10 or 11^16*17^10. Here are the prime factorizations for the first 48 elements of RF11: (11^10), (11^10)*(13^10), (11^10)*(17^10), (11^10)*(19^10), (11^10)*(13^12), (11^10)*(23^10), (11^10)*(29^10), (11^10)*(31^10), (11^10)*(37^10), (11^10)*(41^10), (11^10)*(43^10), (11^10)*(47^10), (11^10)*(53^10), (11^10)*(59^10), (11^10)*(61^10), (11^10)*(67^10), (11^10)*(71^10), (11^10)*(73^10), (11^10)*(79^10), (11^10)*(83^10), (11^10)*(89^10), (11^10)*(17^16), (11^10)*(97^10), (11^10)*(101^10), (11^10)*(103^10), (11^10)*(107^10), (11^10)*(109^10), (11^10)*(113^10), (11^10)*(127^10), (11^10)*(131^10), (11^10)*(137^10), (11^10)*(139^10), (11^10)*(149^10), (11^10)*(151^10), (11^10)*(157^10), (11^10)*(163^10), (11^10)*(167^10), (11^10)*(173^10), (11^10)*(179^10), (11^10)*(181^10), (11^10)*(191^10), (11^10)*(193^10), (11^10)*(197^10), (11^10)*(199^10), (11^10)*(211^10), (11^10)*(13^10)*(17^10), (11^10)*(2 23^10), (11^10)*(227^10).

Examples

			a(1)=11^(11-1)=25937424601.
		

Crossrefs

Cf. A033950, A036896, A036897.

Programs

Maple

with(numtheory); p:=11: a:=p^(p-1): RF11:=[a]: P:=[seq(ithprime(i),i=2..pi(p)-1)]; for w to 1 do for j from 1 to 12^3 do k:=2*j+1; if andmap(z -> k mod z <> 0, P) then for s from 2 to p-1 by 2 do #accelerate creation n:=a*k^s; t:=tau(n); if not n in RF11 and (n mod t = 0) then RF11:=[op(RF11),n]; print(ifactor(n)); fi; od; fi; od od; RF11:=sort(RF11);

Formula

a(n) = odd square, 11 is the smallest prime factor and refactorable.