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A247603 Least integer m > 0 with pi(m*n) = sigma(m), where sigma(m) is the sum of all positive divisors of m. 7
1, 2, 23, 61, 8, 22, 16, 12, 202, 386, 30, 36, 174, 10745, 1684, 2804, 1616, 40006, 6764, 996, 5775, 8131355, 19974, 11264, 4446, 27882, 4848, 32466, 162712, 532313373, 2341816, 30864, 14544, 63696, 2880, 390990, 135200, 133992, 1331840, 11621646, 117990 (list; graph; refs; listen; history; text; internal format)
OFFSET

2,2

COMMENTS

Conjecture: a(n) exists for any n > 1.

LINKS

Hiroaki Yamanouchi, Table of n, a(n) for n = 2..53

Zhi-Wei Sun, A new theorem on the prime-counting function, arXiv:1409.5685, 2014.

EXAMPLE

a(3) = 2 since pi(3*2) = 3 = sigma(2), and pi(3*1) = 2 > sigma(1) = 1.

MATHEMATICA

Do[m=1; Label[aa]; If[PrimePi[n*m]==DivisorSigma[1, m], Print[n, " ", m]; Goto[bb]]; m=m+1; Goto[aa];

Label[bb]; Continue, {n, 2, 30}]

CROSSREFS

Cf. A000203, A000720, A247600, A247601, A247602, A247604, A247672, A247673.

Sequence in context: A070934 A296272 A031915 * A102385 A290226 A214596

Adjacent sequences:  A247600 A247601 A247602 * A247604 A247605 A247606

KEYWORD

nonn

AUTHOR

Zhi-Wei Sun, Sep 21 2014

EXTENSIONS

a(31)-a(42) from Hiroaki Yamanouchi, Oct 04 2014

STATUS

approved

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Last modified November 18 09:46 EST 2019. Contains 329261 sequences. (Running on oeis4.)