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bibkey: seidov2006a119623 authors: Zak Seidov year: 2006 title: “OEIS A119623, Composite numbers for which the second elementary symmetric function of divisors is prime” doi: null url: https://oeis.org/A119623 claim: “A119623 %N (Zak Seidov, Jun 08 2006): Composite numbers for which the second elementary symmetric function of divisors (s2) is prime. A119623 %C (Zak Seidov, Jun 08 2006): Terms in A119616 are always prime if n is prime p and s2(p)=p, hence it is interesting to find composite numbers for which s2 is also prime. Relative values of s2 are: s2=47,97,163,457,733,2203,3733,7993,10723,11317,21313,22147,26557,33403,57283,61417,67153,79393,101467,149323,160453,162727,174337,272683,296827,318793,358273,432907,440383,486583,551767,639007,832687,843043,911917,961183,1152913,1202017,1277593,1322743,1375303,1462897,1567327,1824997,1878883. Otherwise the sequence s2 gives numbers which appear in A119616 at least twice (and conjecture is that exactly twice). A119616 %N (N. J. A. Sloane, based on email from Neven Juric, Jun 07 2006): Second elementary symmetric function of divisors of n.” strata_touched:

  • D5/S1/Recurrence/Invariants/DivisorPairProductPrimePreimages license: citation-only triage: anchor

OEIS A119623

Zak Seidov’s 2006 entry records the composite arguments at which the second elementary symmetric function of the positive divisors is prime. The linked A119616 entry defines that function and gives the equivalent formula a(n) = Sum_{u|n, v|n, u<v} u*v.

For a prime argument p, A119616 records s2(p)=p. Thus every prime value attained at a composite argument already has the prime argument as a second preimage. Seidov’s comment conjectures that these are the only two preimages.

Verified locator

  • URL: https://oeis.org/A119623

  • A119623 COMMENTS, Zak Seidov, Jun 08 2006:

    Terms in A119616 are always prime if n is prime p and s2(p)=p, hence it is interesting to find composite numbers for which s2 is also prime. Relative values of s2 are: s2=47,97,163,457,733,2203,3733,7993,10723,11317,21313,22147,26557,33403,57283,61417,67153,79393,101467,149323,160453,162727,174337,272683,296827,318793,358273,432907,440383,486583,551767,639007,832687,843043,911917,961183,1152913,1202017,1277593,1322743,1375303,1462897,1567327,1824997,1878883. Otherwise the sequence s2 gives numbers which appear in A119616 at least twice (and conjecture is that exactly twice).

  • A119616 NAME:

    Second elementary symmetric function of divisors of n.