A055470 - OEIS

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A055470

Smallest number x>1 such that Phi(x)+Sigma(x) = k*d(x)^n, i.e. the left-hand side is divisible by the n-th power of the number of divisors.

2, 2, 95, 121, 121, 2047, 49151, 98303, 393215, 1572863, 6291455, 8388607, 201326591, 805306367, 3221225471, 6442450943, 137438953471, 137438953471, 137438953471 (list; graph; refs; listen; history; internal format)

	OFFSET	`1,1`
	COMMENTS	`It appears that for n>5, a(n) is a semiprime. - Lambert Klasen (Lambert.Klasen(AT)gmx.net), Aug 22 2005` `a(20) <= 2199023255551. a(21) <= 2199023255551. - Donovan Johnson, Jun 05 2011`
	FORMULA	`Least integer x>1 such that A000010(x)+A000203(x) = k*A000005(x)^n`
	EXAMPLE	`The terms of list {2,2,95,121,121,2047,49151,98303} have {2,2,4,3,3,4,4,4} divisors, {3,3,120,133,133,2160,51312,99000} divisor-sums, {1,1,72,110,110,1936,46992,97608} EulerPhi values. The Phi+Sigma Sums are {4,4,192,243,243,4096,98304,196608}, which are divided by {2,4,64,81,243,4096,16384,65536} increasing powers of d-numbers, giving {2,1,3,3,1,1,6,3} quotients respectively.`
	PROG	`(PARI) k=2; for(n=1, 15, while(denominator((sigma(k)+eulerphi(k))/(sigma(k, 0)^n))!=1, k++); \ print(n, " ", k)) (Klasen)`
	CROSSREFS	`Cf. A000203, A000010, A000005.` `Sequence in context: A156511 A166996 A133295 * A156524 A194027 A003110` `Adjacent sequences: A055467 A055468 A055469 * A055471 A055472 A055473`
	KEYWORD	`nonn`
	AUTHOR	`Labos E. (labos(AT)ana.sote.hu), Jun 27 2000`
	EXTENSIONS	`More terms from Jud McCranie (JudMcCranie(AT)ugaalum.uga.edu), Oct 08 2000` `More terms from Lambert Klasen (Lambert.Klasen(AT)gmx.net), Aug 22 2005` `a(16)-a(19) from Donovan Johnson (donovan.johnson(AT)yahoo.com), Jun 05 2011`

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Last modified February 15 02:50 EST 2012. Contains 205694 sequences.